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## Curvature singularities: The good, the bad, and the naked (2002)

Venue: | Adv. Theor. Math. Phys |

Citations: | 98 - 7 self |

### Citations

5605 | The large N limit of superconformal field theories and supergravity
- Maldacena
- 1998
(Show Context)
Citation Context ...o be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem. February 20001 Introduction In AdS/CFT =-=[1, 2, 3]-=- (see [4] for a review), bulk geometries which are only asymptotically AdS5 near the timelike boundary are dual to relevant deformations of the CFT or to non-conformal vacua. Far from the timelike bou... |

2744 |
Gauge theory correlators from noncritical string theory.” Phys. Lett. B428
- Gubser, Klebanov, et al.
- 1998
(Show Context)
Citation Context ...o be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem. February 20001 Introduction In AdS/CFT =-=[1, 2, 3]-=- (see [4] for a review), bulk geometries which are only asymptotically AdS5 near the timelike boundary are dual to relevant deformations of the CFT or to non-conformal vacua. Far from the timelike bou... |

2334 |
Anti-de Sitter space and holography
- Witten
- 1998
(Show Context)
Citation Context ...o be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem. February 20001 Introduction In AdS/CFT =-=[1, 2, 3]-=- (see [4] for a review), bulk geometries which are only asymptotically AdS5 near the timelike boundary are dual to relevant deformations of the CFT or to non-conformal vacua. Far from the timelike bou... |

1435 | Large N field theories, string theory and gravity
- Aharony, Gubser, et al.
(Show Context)
Citation Context ...Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem. February 20001 Introduction In AdS/CFT [1, 2, 3] (see =-=[4]-=- for a review), bulk geometries which are only asymptotically AdS5 near the timelike boundary are dual to relevant deformations of the CFT or to non-conformal vacua. Far from the timelike boundary, va... |

1080 | Anti-de Sitter space, thermal phase transition, and confinement in gauge theories
- Witten
- 1998
(Show Context)
Citation Context ...ppropriately defined one-dimensional Schrodinger hamiltonian. This identification is a direct consequence of the prescription of [2, 3], and it is the basis of all AdS-glueball calculations following =-=[61, 62]-=-. Since it has been discussed, implicitly or explicitly, in many other places in the literature (for instance [61, 62, 8, 9, 63]) we can afford to be brief. Our aim is simply to make the discussion of... |

675 | Superconformal field theory on threebranes at a CalabiYau singularity - Klebanov, Witten - 1998 |

529 |
Monopoles, duality and chiral symmetry breaking
- Seiberg, Witten
- 1994
(Show Context)
Citation Context ... these flows, inspired by [37], though it must be regarded as speculative in the absence of more detailed tests. The far infrared theory is large-N Seiberg-Witten theory, and the Seiberg-Witten curve =-=[45]-=- is [46, 47] y 2 N∏ = (x − ξk) k=1 2 − Λ 2N , (45) where Λ is the dynamically generated scale and ξk are parameters determining the position on the moduli space. In [37] it was suggested that the enha... |

323 | Some properties of Noether charge and a proposal for dynamical black hole entropy,” Phys
- Iyer, Wald
- 1994
(Show Context)
Citation Context ...ore curvatures become Planckian? The horizon area per unit volume at r = rH is e 3A(rH) . The entropy formula is actually more complicated than S = A/4G5 when higher derivative terms become important =-=[66, 67, 68]-=-, but to obtain a rough-and-ready estimate we will stick with the simple area law. (For nearextremal D3-branes with no evolving scalars, the evidence of AdS/CFT is that all the α ′ corrections only ch... |

292 | Renormalization group flows from holography supersymmetry and a c theorem
- Freedman, Gubser, et al.
- 1999
(Show Context)
Citation Context ...N = 4 super-Yang-Mills theory [6, 7, 8, 9, 10], and are also suspected to be the supergravity duals of most renormalization group flows arising from relevant deformations of the lagrangian of the CFT =-=[11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]-=-. The classical equations of motion, plus either positivity of the scalar kinetic terms or the more general “null energy” condition, together imply A ′′ (r) ≤ 0 [14, 18]. Since we assume A(r) ∼ r/L wi... |

235 |
Strong Coupling Expansion Of Calabi-Yau Compactification, Nucl
- Witten
- 1996
(Show Context)
Citation Context ...ure singularity parallel to the brane on which visible sector matter exists, at some finite proper distance from it. Such constructions were first considered in the context of Horava-Witten theory in =-=[77]-=-. They have also appeared as a variant of the Randall-Sundrum construction (see for instance [78]). Following in the spirit of [79], it was recently proposed by two Stanford groups [80, 81] that such ... |

228 |
Modeling the fifth dimension with scalars and gravity
- DeWolfe, Freedman, et al.
(Show Context)
Citation Context ...ix Wab, defined on E6(6)/USp(8), which serves as a generalized superpotential in the sense that the gravitino variation has the form δψµa = Dµǫa − 1 6 gWabγµǫ b (see [29, 18] for further details). In =-=[31, 32, 33]-=-, the form (4) was found to be useful, independent of supersymmetry, for generating solutions of the form (1) and investigating their properties. Indeed, given 4V (⃗ϕ), the equation (4) can be regard... |

225 |
Charged AdS black holes and catastrophic holography,”
- Chamblin, Emparan, et al.
- 1999
(Show Context)
Citation Context ...J56. In five dimensions these angular momenta are interpreted as charges under the U(1) 3 Cartan subalgebra of the SO(6) gauge group, and the spinning D3-branes are represented as charged black holes =-=[41, 42]-=-. The time components of the gauge fields in five-dimensional supergravity act as “voltages,” or “chemical potentials,” for conserved R-currents in the gauge theory. The positive and negative ϕ2 flows... |

196 | Lectures on supersymmetric gauge theories and electric - magnetic duality,” Nucl. Phys
- Intriligator, Seiberg
- 1996
(Show Context)
Citation Context ...ng to the standard analysis is 〈trλ4λ4〉 ≈ c2e 2πik/N NΛ 3 , (52) where c2 is another constant of order unity, Λ is the scale of the low-energy N = 1 theory, and k can run from 1 to N (see for example =-=[50, 51, 52, 53, 54, 55]-=-). Again up to factors of order unity, Λ = m exp ( − 8π2 3g2 ) where g is the gauge coupling at the N N = 4 ultraviolet fixed point. The overall factor of N in (52) ensures that domain walls between a... |

174 | The Holographic Bound in Anti-de Sitter Space
- Susskind, Witten
(Show Context)
Citation Context ...A(r) ∼ r/L with L > 0 for large r, A(r) must in fact be monotonically increasing with r. Thus a curvature singularity can arise for the metric (1) if A(r) → −∞ at some finite r0. 1 The UV-IR relation =-=[27, 28]-=- suggests that curvature singularities that arise as A(r) → −∞ represent non-trivial infrared physics in the dual field theory. (Recall that A(r) = 1 2 log |gtt| is roughly the log of the energy scale... |

156 |
Supersymmetric Yang-Mills theory and integrable systems
- Donagi, Witten
- 1996
(Show Context)
Citation Context ...g equal but opposite masses to two adjoint chiral multiplets, which we take to be Φ1 and Φ2—exactly the chiral adjoints which we left massless in the previous example. The field theory was studied in =-=[44]-=-. The supergravity [40] involves the same scalar ϕ2 in the 20 ′ of SO(6) as we had in the previous example, but a different scalar ˜ϕ3 in the 10 + 10. The dual operators are O2 = tr ( −X 2 1 − X2 2 − ... |

151 |
Gauge theory and the excision of repulson singularities, Phys. Rev D61
- Johnson, Peet, et al.
- 2000
(Show Context)
Citation Context ...fted to ten dimensions: the brane distributions involve branes both of positive tension and positive charge, and of negative tension and negative charge. A similar problem was beautifully resolved in =-=[37]-=-, but for Coulomb branch states it is obscure what enhancement of symmetry could play a relevant role. In section 4 we will encounter other pathologies in geometries which violate (2). In short, it se... |

150 |
A correspondence principle for black holes and strings
- Horowitz, Polchinski
- 1997
(Show Context)
Citation Context ... at a singularity which applies beyond the applicability of supergravity, there should be a smooth match from the microscopic description to the black hole horizon description at some crossover point =-=[38]-=-. 2) Numerical studies of two examples for which the field theory dual is reasonably well-understood indeed exhibit a smooth limit in which black hole solutions converge to a Poincaré invariant soluti... |

136 | Nekrasov, Gravity duals of fractional branes and logarithmic - Klebanov, A - 2000 |

132 |
Tseytlin, “Coupling constant dependence
- Gubser, Klebanov, et al.
- 1998
(Show Context)
Citation Context ...stick with the simple area law. (For nearextremal D3-branes with no evolving scalars, the evidence of AdS/CFT is that all the α ′ corrections only change the area law by 4/3 in the α ′ /L 2 → ∞ limit =-=[69, 70]-=-. However a “phase transition” at finite α ′ /L 2 cannot be ruled out [71].) In units where L = 1, we have 1/G5 = N 2 , so the entropy per unit volume is roughly N 2 e 3A(rH) . Assuming that near-extr... |

120 | The Coulomb branch of gauge theory from rotating branes
- Kraus, Larsen, et al.
- 1999
(Show Context)
Citation Context ...of curvature of the asymptotically AdS5 region. Geometries of the form (1) arise in the gauged supergravity description of certain vacuum states on the Coulomb branch of N = 4 super-Yang-Mills theory =-=[6, 7, 8, 9, 10]-=-, and are also suspected to be the supergravity duals of most renormalization group flows arising from relevant deformations of the lagrangian of the CFT [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2... |

118 | Black hole entropy and highercurvature interactions,”
- Jacobson, Myers
- 1993
(Show Context)
Citation Context ...ore curvatures become Planckian? The horizon area per unit volume at r = rH is e 3A(rH) . The entropy formula is actually more complicated than S = A/4G5 when higher derivative terms become important =-=[66, 67, 68]-=-, but to obtain a rough-and-ready estimate we will stick with the simple area law. (For nearextremal D3-branes with no evolving scalars, the evidence of AdS/CFT is that all the α ′ corrections only ch... |

115 |
AdS/CFT correspondence and symmetry breaking,” Nucl. Phys. B556
- Klebanov, Witten
- 1999
(Show Context)
Citation Context ...of curvature of the asymptotically AdS5 region. Geometries of the form (1) arise in the gauged supergravity description of certain vacuum states on the Coulomb branch of N = 4 super-Yang-Mills theory =-=[6, 7, 8, 9, 10]-=-, and are also suspected to be the supergravity duals of most renormalization group flows arising from relevant deformations of the lagrangian of the CFT [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2... |

113 |
Gravitational stability and renormalization-group
- Skenderis, Townsend
- 1999
(Show Context)
Citation Context ...ix Wab, defined on E6(6)/USp(8), which serves as a generalized superpotential in the sense that the gravitino variation has the form δψµa = Dµǫa − 1 6 gWabγµǫ b (see [29, 18] for further details). In =-=[31, 32, 33]-=-, the form (4) was found to be useful, independent of supersymmetry, for generating solutions of the form (1) and investigating their properties. Indeed, given 4V (⃗ϕ), the equation (4) can be regard... |

101 | Brane cosmological evolution in a bulk with cosmological constant,” - Binetruy, Deffayet, et al. - 2000 |

100 |
Phases of R-charged black holes, spinning branes and strongly coupled gauge theories,”
- Cvetic, Gubser
- 1999
(Show Context)
Citation Context ...J56. In five dimensions these angular momenta are interpreted as charges under the U(1) 3 Cartan subalgebra of the SO(6) gauge group, and the spinning D3-branes are represented as charged black holes =-=[41, 42]-=-. The time components of the gauge fields in five-dimensional supergravity act as “voltages,” or “chemical potentials,” for conserved R-currents in the gauge theory. The positive and negative ϕ2 flows... |

97 | Glueball mass spectrum from supergravity
- Csaki, Ooguri, et al.
- 1999
(Show Context)
Citation Context ...ppropriately defined one-dimensional Schrodinger hamiltonian. This identification is a direct consequence of the prescription of [2, 3], and it is the basis of all AdS-glueball calculations following =-=[61, 62]-=-. Since it has been discussed, implicitly or explicitly, in many other places in the literature (for instance [61, 62, 8, 9, 63]) we can afford to be brief. Our aim is simply to make the discussion of... |

92 |
Compact and Noncompact Gauged Supergravity Theories
- Günaydin, Romans, et al.
- 1986
(Show Context)
Citation Context ...(⃗ϕ) . (3) Usually it will be assumed that the potential V (⃗ϕ) has a local maximum at ⃗ϕ = 0. Our main example of such an action is the gravity-plus-scalars sector of d = 5 N = 8 gauged supergravity =-=[29, 30]-=-. Here the 42 scalars ⃗ϕ parametrize the coset E6(6)/USp(8), and V (⃗ϕ) is a SO(6) × SL(2,R)-invariant function on this coset. The kinetic term would be more accurately represented as GIJ(⃗ϕ)∂ϕ I ∂ϕ J... |

90 | D.: Stability in gauged extended supergravity - Breitenlohner, Freedman - 1982 |

86 |
Anomalous Supersymmetry Transformation Of Some Composite Operators
- Konishi
- 1984
(Show Context)
Citation Context ...ng to the standard analysis is 〈trλ4λ4〉 ≈ c2e 2πik/N NΛ 3 , (52) where c2 is another constant of order unity, Λ is the scale of the low-energy N = 1 theory, and k can run from 1 to N (see for example =-=[50, 51, 52, 53, 54, 55]-=-). Again up to factors of order unity, Λ = m exp ( − 8π2 3g2 ) where g is the gauge coupling at the N N = 4 ultraviolet fixed point. The overall factor of N in (52) ensures that domain walls between a... |

85 |
A small cosmological constant from a large extra dimension”, Phys. Lett. B480
- Arkani-Hamed, Dimopoulos, et al.
- 2000
(Show Context)
Citation Context ...tten theory in [77]. They have also appeared as a variant of the Randall-Sundrum construction (see for instance [78]). Following in the spirit of [79], it was recently proposed by two Stanford groups =-=[80, 81]-=- that such geometries could help solve the cosmological constant problem. In this appendix we will consider only the minimal case where the “Planck brane” is at one end of the spacetime, where gtt is ... |

74 | Nonsupersymmetric conformal field theories from stable anti-de Sitter spaces
- Distler, Zamora
- 1999
(Show Context)
Citation Context ...N = 4 super-Yang-Mills theory [6, 7, 8, 9, 10], and are also suspected to be the supergravity duals of most renormalization group flows arising from relevant deformations of the lagrangian of the CFT =-=[11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]-=-. The classical equations of motion, plus either positivity of the scalar kinetic terms or the more general “null energy” condition, together imply A ′′ (r) ≤ 0 [14, 18]. Since we assume A(r) ∼ r/L wi... |

69 |
Self-tuning flat domain walls in 5d gravity and string theory, hep-th/0001206
- Kachru, Schulz, et al.
(Show Context)
Citation Context ...imensional Poincaré invariance. But it seems implausible that the tension of an end-of-the-universe brane after supersymmetry breaking would solve the equation (65) identically. The generalization of =-=[81]-=- is to demand only that W(⃗ϕ) and ±λPl(⃗ϕ) are tangent at some point. This requires exactly one fine-tuning if W(⃗ϕ) is regarded as a fixed 10 I thank M. Peskin and R. Sundrum for comments on this poi... |

64 |
Wilson loops from multicentre and rotating branes, mass gaps and phase structure in gauge theories
- Brandhuber, Sfetsos
- 1999
(Show Context)
Citation Context ...ription of [2, 3], and it is the basis of all AdS-glueball calculations following [61, 62]. Since it has been discussed, implicitly or explicitly, in many other places in the literature (for instance =-=[61, 62, 8, 9, 63]-=-) we can afford to be brief. Our aim is simply to make the discussion of [8] more systematic. Consider a Poincaré invariant flow solution of the form (1). It is convenient to introduce a new radial va... |

63 | Symmetric potentials of gauged supergravities in diverse dimensions and Coulomb branch of gauge theories,” Phys
- Cvetič, Gubser, et al.
- 2000
(Show Context)
Citation Context ...of curvature of the asymptotically AdS5 region. Geometries of the form (1) arise in the gauged supergravity description of certain vacuum states on the Coulomb branch of N = 4 super-Yang-Mills theory =-=[6, 7, 8, 9, 10]-=-, and are also suspected to be the supergravity duals of most renormalization group flows arising from relevant deformations of the lagrangian of the CFT [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2... |

62 |
The supergravity dual of
- Girardello, Petrini, et al.
(Show Context)
Citation Context ...N = 4 super-Yang-Mills theory [6, 7, 8, 9, 10], and are also suspected to be the supergravity duals of most renormalization group flows arising from relevant deformations of the lagrangian of the CFT =-=[11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]-=-. The classical equations of motion, plus either positivity of the scalar kinetic terms or the more general “null energy” condition, together imply A ′′ (r) ≤ 0 [14, 18]. Since we assume A(r) ∼ r/L wi... |

61 |
Dynamics in nonglobally hyperbolic static space-times.
- Ishibashi, Wald
- 2004
(Show Context)
Citation Context ...) This leads to m 2 L 2 ≥ −4 by a standard Bessel function analysis. For geometries with naked singularities, the positivity of the Schrodinger operator in (58) is essentially a condition proposed in =-=[64]-=- almost twenty years ago, and also considered in [65]. 7 With trivial adaptations appropriate to the current context, the contents of [64] can be summarized as follows. The Schrodinger operator on the... |

60 |
Continuous distributions of D3-branes and gauged supergravity,” hep-th/9906194
- Freedman, Gubser, et al.
(Show Context)
Citation Context |

58 |
The vacuum structure and spectrum of N=2 supersymmetric SU(n) gauge theory
- Argyres, Faraggi
- 1995
(Show Context)
Citation Context ...lows, inspired by [37], though it must be regarded as speculative in the absence of more detailed tests. The far infrared theory is large-N Seiberg-Witten theory, and the Seiberg-Witten curve [45] is =-=[46, 47]-=- y 2 N∏ = (x − ξk) k=1 2 − Λ 2N , (45) where Λ is the dynamically generated scale and ξk are parameters determining the position on the moduli space. In [37] it was suggested that the enhançon singula... |

56 |
Simple singularities and N=2 supersymmetric Yang-Mills theory,” Phys
- Klemm, Lerche, et al.
- 1995
(Show Context)
Citation Context ...lows, inspired by [37], though it must be regarded as speculative in the absence of more detailed tests. The far infrared theory is large-N Seiberg-Witten theory, and the Seiberg-Witten curve [45] is =-=[46, 47]-=- y 2 N∏ = (x − ξk) k=1 2 − Λ 2N , (45) where Λ is the dynamically generated scale and ξk are parameters determining the position on the moduli space. In [37] it was suggested that the enhançon singula... |

55 |
Stability at a Local Maximum in Higher Dimensional Anti-de Sitter Space and Applications to Supergravity
- Mezincescu, Townsend
- 1985
(Show Context)
Citation Context ...s means the effective potential Veff in the field theory is unbounded below. This pathology manifests itself in five-dimensional gauged supergravity as a violation of the Breitenlohner-Freedman bound =-=[34, 35]-=- at the SO(5) critical point. Another pathology which one could imagine in field theory is attempting to assign a negative vacuum 5expectation value (VEV) to a positive definite operator. In section ... |

54 |
New vacua of gauged N = 8 supergravity in five dimensions, hep-th/9812035
- Khavaev, Pilch, et al.
- 1999
(Show Context)
Citation Context |

47 |
Nonstandard compactifications with mass gaps and Newton’s law,” hep-th/9908116
- Brandhuber, Sfetsos
(Show Context)
Citation Context ...r distance from it. Such constructions were first considered in the context of Horava-Witten theory in [77]. They have also appeared as a variant of the Randall-Sundrum construction (see for instance =-=[78]-=-). Following in the spirit of [79], it was recently proposed by two Stanford groups [80, 81] that such geometries could help solve the cosmological constant problem. In this appendix we will consider ... |

46 |
The value of singularities
- Horowitz, Myers
- 1995
(Show Context)
Citation Context ...There must be some restrictions on the type of singularity which is allowed: for instance, we take it as obvious that negative mass Schwarzschild should be excluded on the grounds of vacuum stability =-=[5]-=-. The goal of this paper is to address the question of what singularities are allowed in geometries of the form ds 2 = e 2A(r) (−dt 2 + d⃗x 2 ) + dr 2 ⃗ϕ = ⃗ϕ(r) , (1) where by assumption A(r) ∼ r/L a... |

46 | Mirage cosmology,” - Kehagias, Kiritsis - 1999 |

45 |
The universe as a domain wall, Phys. Rev. D59
- Lukas, Ovrut, et al.
- 1999
(Show Context)
Citation Context ...ible to rule out all the C2 > 3C1 trajectories, since they have the same behavior in the infrared. Incidentally, the “universal solution” of Horava-Witten theory compactified on a Calabi-Yau manifold =-=[58]-=- develops the same singularity as the C2 > 3C1 flows if the negative tension “hidden sector” end-of-the-world brane is taken to infinite redshift. The low-energy limit of the hidden sector gauge theor... |

44 |
On running couplings in gauge theories from type-IIB supergravity,” Phys
- Kehagias, Sfetsos
- 1999
(Show Context)
Citation Context ... have been claimed to exhibit properties of confinement [72, 73, 74, 19], but the case for confinement in those examples was less than airtight. It is particularly easy to show that the geometries of =-=[75, 73]-=-, involving only the metric and the dilaton, cannot support a black hole horizon. The scalar equation of motion plus the horizon boundary conditions imply that the dilaton is everywhere constant. The ... |

43 |
A strong coupling test of S duality,” Nucl. Phys. B431
- Vafa, Witten
- 1994
(Show Context)
Citation Context ...r 2 i Φ2 i . Naively, the infrared theory is N = 1 super-QCD. In fact, the model has many vacua, corresponding to non-commutative VEV’s for the massive scalars φi which form a representation of SU(2) =-=[48, 44]-=-. The deformation of the lagrangian consists of a dimension 3 operator, which preserves SO(3) and gives a uniform mass to three adjoint fermions; and a dimension 2 operator, which is just the SO(6) sy... |

35 |
States and Curves of Five-Dimensional Gauged Supergravity, Nucl. Phys. B573 (2000) 768 [hep-th/9909041]; Domain walls of gauged supergravity, M-branes, and algebraic curves, Fortsch. Phys. 48
- Bakas, Sfetsos
- 2000
(Show Context)
Citation Context ... assert that not all naked singularities are physical, even if we demand 3 + 1-dimensional Poincaré invariance and/or some unbroken supersymmetry. Indeed, some of the Coulomb branch flows explored in =-=[8, 36, 10]-=- have an unphysical property when they were lifted to ten dimensions: the brane distributions involve branes both of positive tension and positive charge, and of negative tension and negative charge. ... |

35 | Asymptotic freedom and confinement from type 0 string theory, JHEP 04
- Minahan
- 1999
(Show Context)
Citation Context ...he dual field theory, and that they can never support finite temperature. This unfortunately tells against some supergravity constructions which have been claimed to exhibit properties of confinement =-=[72, 73, 74, 19]-=-, but the case for confinement in those examples was less than airtight. It is particularly easy to show that the geometries of [75, 73], involving only the metric and the dilaton, cannot support a bl... |

27 |
Confinement and condensates without fine tuning in supergravity duals of gauge theories, JHEP 9905
- Girardello, Petrini, et al.
- 1999
(Show Context)
Citation Context ...he dual field theory, and that they can never support finite temperature. This unfortunately tells against some supergravity constructions which have been claimed to exhibit properties of confinement =-=[72, 73, 74, 19]-=-, but the case for confinement in those examples was less than airtight. It is particularly easy to show that the geometries of [75, 73], involving only the metric and the dilaton, cannot support a bl... |

24 |
A new constraint on strongly coupled field theories.
- Appelquist, Cohen, et al.
- 1999
(Show Context)
Citation Context ... that in the range where (34) predicts positive specific heats, it also predicts that −F/T 4 is an increasing function of temperature. This is consistent with the Appelquist-Cohen-Schmaltz conjecture =-=[39]-=-. 3 √ For ζ > 2/3, the evidence of (34) is that T → ∞ as rH → r0. It could be that instead T remains finite in this limit. Either of these two outcomes would signal a finite temperature phase transiti... |

19 |
and the dynamics of QCD,” Nucl. Phys. B507
- Witten, “Branes
- 1997
(Show Context)
Citation Context ...otential has one more power of N than the gaugino condensate; but domain wall tensions are given by the change of W across the domain wall, and W changes by a phase e2πi/N from one vacuum to the next =-=[56]-=-. Naively, the operator O3 is tr (λ4λ4 + φ1[φ2, φ3]) + h.c., as in (37). Both the fermion bilinear and the scalar trilinear are manifestly SU(3) invariant. The VEV of the first term in the trivial vac... |

19 |
On asymptotic freedom and confinement from typeIIB supergravity,” Phys
- Kehagias, Sfetsos
- 1999
(Show Context)
Citation Context ...he dual field theory, and that they can never support finite temperature. This unfortunately tells against some supergravity constructions which have been claimed to exhibit properties of confinement =-=[72, 73, 74, 19]-=-, but the case for confinement in those examples was less than airtight. It is particularly easy to show that the geometries of [75, 73], involving only the metric and the dilaton, cannot support a bl... |

18 |
D3-brane shells to black branes on the Coulomb branch
- Giddings, Ross
(Show Context)
Citation Context ...with this behavior arise in certain U(1) gauged supergravities. Second, an S 5 shell of D3-branes produces a near-horizon geometry which is AdS5 × S 5 outside the shell and flat R 10 inside the shell =-=[24, 25]-=-. The shell itself produces a curvature singularity at finite A(r). Similar singularities arise in Horava-Witten theory compactified on a Calabi-Yau three-fold with M5-branes in the bulk (see for exam... |

18 |
Domain walls of D = 5 supergravity and fixed points of
- Behrndt
- 2000
(Show Context)
Citation Context ...vacuum state in these solutions may simplify the interpretation of the holographic renormalization group proposed in [22]. For instance, the identification of beta functions with gradients of scalars =-=[76, 22]-=- seems odd in Coulomb branch states of N = 4 gauge theory, but possibly more natural for mass deformations in some preferred vacuum. A true acid test for the subject would be to reproduce some known q... |

17 | Brane-world solutions, standard cosmology, and dark radiation”, Phys - Mukohyama - 2000 |

16 |
On black hole entropy, Phys. Rev. D49
- Jacobson, Kang, et al.
- 1994
(Show Context)
Citation Context ...ore curvatures become Planckian? The horizon area per unit volume at r = rH is e 3A(rH) . The entropy formula is actually more complicated than S = A/4G5 when higher derivative terms become important =-=[66, 67, 68]-=-, but to obtain a rough-and-ready estimate we will stick with the simple area law. (For nearextremal D3-branes with no evolving scalars, the evidence of AdS/CFT is that all the α ′ corrections only ch... |

15 |
Generalized conifolds and four dimensional
- Gubser, Nekrasov, et al.
- 1999
(Show Context)
Citation Context |

15 |
Exact superpotentials
- Intriligator, Leigh, et al.
- 1994
(Show Context)
Citation Context ...ng to the standard analysis is 〈trλ4λ4〉 ≈ c2e 2πik/N NΛ 3 , (52) where c2 is another constant of order unity, Λ is the scale of the low-energy N = 1 theory, and k can run from 1 to N (see for example =-=[50, 51, 52, 53, 54, 55]-=-). Again up to factors of order unity, Λ = m exp ( − 8π2 3g2 ) where g is the gauge coupling at the N N = 4 ultraviolet fixed point. The overall factor of N in (52) ensures that domain walls between a... |

13 |
New N = 1 superconformal field theories and their supergravity description, Phys
- Karch, Lüst, et al.
- 1999
(Show Context)
Citation Context |

13 |
On gluino condensation in supersymmetric gauge theories SU(N) and O(N) groups,
- Shifman, Vainshtein
- 1988
(Show Context)
Citation Context |

12 |
Chiral symmetry breaking
- Distler, Zamora
(Show Context)
Citation Context ...ich violate the BreitenlohnerFreedman bound [34, 35]. Two well-known examples are flows to the SO(5) symmetric critical point of d = 5 N = 8 gauged supergravity, and flows to the SU(3) critical point =-=[14, 15, 59, 60]-=-. We would like to have a generalization of the BreitenlohnerFreedman bound which applies to cases which are only asymptotically AdS5 in the ultraviolet. The obvious one is to demand that the spectral... |

10 |
On the Holographic Renormalization Group,” hep-th/9912012
- Boer, Verlinde, et al.
- 1998
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10 |
A note on correlation functions
- Chepelev, Roiban
- 1999
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Citation Context ...with this behavior arise in certain U(1) gauged supergravities. Second, an S 5 shell of D3-branes produces a near-horizon geometry which is AdS5 × S 5 outside the shell and flat R 10 inside the shell =-=[24, 25]-=-. The shell itself produces a curvature singularity at finite A(r). Similar singularities arise in Horava-Witten theory compactified on a Calabi-Yau three-fold with M5-branes in the bulk (see for exam... |

10 |
Exact results in gauge theories: putting super-symmetry at work
- Shifman
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10 |
Quantum probes of spacetime singularities, Phys. Rev. D52
- Horowitz, Marolf
- 1995
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Citation Context ...ction analysis. For geometries with naked singularities, the positivity of the Schrodinger operator in (58) is essentially a condition proposed in [64] almost twenty years ago, and also considered in =-=[65]-=-. 7 With trivial adaptations appropriate to the current context, the contents of [64] can be summarized as follows. The Schrodinger operator on the left hand side of (58) is the radial part of a linea... |

10 | Evidence for large N phase transition in N = 4 super Yang- Mills theory at finite temperature”, JHEP 9903, 004
- Li
- 1999
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Citation Context ...calars, the evidence of AdS/CFT is that all the α ′ corrections only change the area law by 4/3 in the α ′ /L 2 → ∞ limit [69, 70]. However a “phase transition” at finite α ′ /L 2 cannot be ruled out =-=[71]-=-.) In units where L = 1, we have 1/G5 = N 2 , so the entropy per unit volume is roughly N 2 e 3A(rH) . Assuming that near-extremal solutions have nearly the same A(rH) as their Poincaré invariant limi... |

8 |
Zakharov, “Instanton Effects In Supersymmetric Theories,” Nucl. Phys
- Novikov, Shifman, et al.
- 1983
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6 |
A Family of N = 1 SU(N)k Theories from Branes at Singularities
- Lopez
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6 |
RG-flow, gravity and the cosmological constant,” hep-th/9912018
- Verlinde, Verlinde
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Citation Context ...ions were first considered in the context of Horava-Witten theory in [77]. They have also appeared as a variant of the Randall-Sundrum construction (see for instance [78]). Following in the spirit of =-=[79]-=-, it was recently proposed by two Stanford groups [80, 81] that such geometries could help solve the cosmological constant problem. In this appendix we will consider only the minimal case where the “P... |

5 |
Non-conformal examples of AdS/CFT, hep-th/9910117
- Gubser
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Citation Context ...ription of [2, 3], and it is the basis of all AdS-glueball calculations following [61, 62]. Since it has been discussed, implicitly or explicitly, in many other places in the literature (for instance =-=[61, 62, 8, 9, 63]-=-) we can afford to be brief. Our aim is simply to make the discussion of [8] more systematic. Consider a Poincaré invariant flow solution of the form (1). It is convenient to introduce a new radial va... |

3 |
Heterotic M-theory vacua with five-branes, Fortsch. Phys
- Lukas, Ovrut, et al.
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Citation Context ...e shell itself produces a curvature singularity at finite A(r). Similar singularities arise in Horava-Witten theory compactified on a Calabi-Yau three-fold with M5-branes in the bulk (see for example =-=[26]-=-): in the five-dimensional description, there is a jump in A ′ (r) across each M5-brane. This sort of singularity also arises in type I ′ with D8-branes in the bulk. Finally, there can be a codimensio... |

3 |
unpublished notes
- Myers
- 1999
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Citation Context ...ix Wab, defined on E6(6)/USp(8), which serves as a generalized superpotential in the sense that the gravitino variation has the form δψµa = Dµǫa − 1 6 gWabγµǫ b (see [29, 18] for further details). In =-=[31, 32, 33]-=-, the form (4) was found to be useful, independent of supersymmetry, for generating solutions of the form (1) and investigating their properties. Indeed, given 4V (⃗ϕ), the equation (4) can be regard... |

2 | Dynamics of anti-de Sitter domain walls,” hep-th/9910149 - Kraus |

2 | The Einstein equation on the 3-brane world,” gr-qc/9910076 - Shiromizu, Maeda, et al. |