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## Holography for chiral scale-invariant models

Venue: | JHEP 1102 (2011) 082, arXiv:1010.4800 [hep-th |

Citations: | 21 - 4 self |

### Citations

453 |
Holographic reconstruction of spacetime and renormalization
- Haro, Solodukhin, et al.
(Show Context)
Citation Context ... [ g(2)ab + 1 2 R(g(0))g(0)ab − z 2 ( b(−z)ab(z)b + b(z)ab(−z)b )− z(z − 1 2 ) ( b(−z)cb c (z) ) g(0)ab ] . Note that the answer for pure Einstein gravity, i.e. when Bm = 0, agrees with that given in =-=[50]-=-. Since the generating functional of the dual field theory W in Lorentzian signature is related to the renormalized on-shell action as W = iSren, these definitions for the operators agree with those g... |

399 |
The holographic Weyl anomaly
- Henningson, Skenderis
- 1998
(Show Context)
Citation Context ...) Db〈Tab〉 = ( b(−z)aD b〈Vb〉+ F b(−z)a〈Vb〉 ) . The relation between the bulk Newton constant G3 and the central charge c of the dual two-dimensional CFT is 1 κ2 = 1 8πG3 = c 24π , (4.21) as derived in =-=[51]-=-. 4.2 Hamiltonian analysis In the previous section we showed that an increasing number of counterterms are needed for z > 1/2. The renormalized one point functions and counterterms are in such cases m... |

300 |
Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry,” Phys
- Son
(Show Context)
Citation Context ...ce in condensed matter physics and as such there would be many interesting applications had one had under control holographic dualities involving non-relativistic QFTs. Motivated by such applications =-=[1, 2]-=- initiated a discussion of holography for (d+ 1) dimensional spacetimes with metric1, ds2 = σ2du2 r2z + 2dudv + dxidxi + dr2 r2 , (1.1) with i ∈ {1, . . . , d− 2}. The isometries of this metric form i... |

280 |
Lecture notes on holographic renormalization
- Skenderis
- 2002
(Show Context)
Citation Context ...e divergences of the on-shell action with covariant counterterms being obtained by inverting these expansions. This method is the most familiar approach to holographic renormalization, see the review =-=[47]-=-, but becomes increasingly cumbersome as the number of counterterms required increases. Since this method works with the asymptotic expansion of the bulk metric and vector, it allows us to appreciate ... |

176 | Comments on string theory backgrounds with non-relativistic conformal symmetry - Maldacena, Martelli, et al. |

169 |
Gravity Duals of Lifshitz-like Fixed
- Kachru, Liu, et al.
(Show Context)
Citation Context ...eodesic incompleteness will not prevent us from computing correlation functions unambiguously in this background, as we will see later; the situation is analogous to that found in Lifshitz spacetimes =-=[22]-=-. Moreover, in section 6 we will see that the geometries can be blackened, with a horizon cloaking the geodesic incompleteness. A singularity is considered acceptable according to the commonly applied... |

117 | Gravity duals for non-relativistic CFTs
- Balasubramanian, McGreevy
- 2009
(Show Context)
Citation Context ...ce in condensed matter physics and as such there would be many interesting applications had one had under control holographic dualities involving non-relativistic QFTs. Motivated by such applications =-=[1, 2]-=- initiated a discussion of holography for (d+ 1) dimensional spacetimes with metric1, ds2 = σ2du2 r2z + 2dudv + dxidxi + dr2 r2 , (1.1) with i ∈ {1, . . . , d− 2}. The isometries of this metric form i... |

98 | Curvature singularities: the good, the bad, and the naked,”
- Gubser
- 2000
(Show Context)
Citation Context ...e that the geometries can be blackened, with a horizon cloaking the geodesic incompleteness. A singularity is considered acceptable according to the commonly applied holographic criteria discussed in =-=[23]-=- if correlation functions can be computed unambiguously and the singularity can be cloaked by a horizon. Precisely this criterion was used in [22] to argue that holography for Lifshitz spacetimes made... |

81 |
Thermodynamics of asymptotically locally AdS spacetimes
- Papadimitriou, Skenderis
- 2005
(Show Context)
Citation Context ...preciate the roles of different terms in the asymptotic expansions, which we will exploit in section 5. The second method of holographic renormalization exploits the Hamiltonian approach developed in =-=[48, 49]-=-, which uses covariant expansions in terms of eigenfunctions of a dilatation operator. This approach is much more efficient and powerful; the main advantage here is that renormalized correlation funct... |

74 | Non-relativistic holography
- Taylor
(Show Context)
Citation Context ...ρ ( dxidx i − σ−2dv 2 ρ ) ; (2.27) A = dv σ2ρ , (2.28) which exhibits Lifshitz symmetry with dynamical exponent ZL = 2 and corresponds to the massive vector model used to obtain Lifshitz solutions in =-=[41]-=-. The Lifshitz symmetry group with dynamical exponent ZL includes a dilatation symmetry ρ→ λ2ρ; v → λZLv; xi → λxi, (2.29) and v is a time coordinate. Note however that strictly speaking the scalar fi... |

70 |
Lifshitz spacetimes from AdS null and cosmological solutions,
- Balasubramanian, Narayan
- 2010
(Show Context)
Citation Context ...eory remains scale invariant; this proof will be discussed in the next section. 3After this paper was published, we became aware of related discussions of null scalar deformations in the earlier work =-=[39]-=-. See also the more recent work [40]. 13 This system is particularly interesting for the following reason. If one considers the case where dF = du, the metric can be written as ds2 = dρ2 4ρ2 + 1 ρ ( d... |

67 |
Consistent supersymmetric Kaluza-Klein truncations with massive modes,
- Gauntlett, Kim, et al.
- 2009
(Show Context)
Citation Context ...ctifications. In the case of z > 1, various embeddings into string theory have been found, with the massive vector actions arising as consistent truncations of type II supergravities, see for example =-=[6, 27, 28, 29, 30, 31, 32, 33, 34, 35]-=-. Note that in these cases the truncation to a graviton and massive vector suffices for the zero temperature background, but additional scalar fields are switched on in the corresponding black hole so... |

66 |
Spectrum of type IIB supergravity on
- Ceresole, Dall’Agata, et al.
(Show Context)
Citation Context ...dual to supergravity modes in Sasaki-Einstein compactifications are however generic. As an example, let us consider the T 1,1 compactification of type IIB supergravity, whose spectrum was computed in =-=[37, 38]-=-. Since T 1,1 is a rank one SU(2)2/U(1) coset, all differential operators can be expressed in terms of the Laplace-Beltrami operator, which is the only functionally independent differential operator. ... |

57 | Precision holography for non-conformal branes
- Kanitscheider, Skenderis, et al.
(Show Context)
Citation Context ... along a spacelike circle will result in a geometry which is conformally asymptotically locally anti-de Sitter in lower dimensions. This fact was used to analyze holography for nonconformal branes in =-=[42, 43]-=-. In the present case, reduction along the circle does not produce a geometry which is conformal to anti-de Sitter, and the reason is that the reduction being carried out is not along a spacelike circ... |

54 | Universal hydrodynamics of non-conformal branes
- Kanitscheider, Skenderis
(Show Context)
Citation Context ... along a spacelike circle will result in a geometry which is conformally asymptotically locally anti-de Sitter in lower dimensions. This fact was used to analyze holography for nonconformal branes in =-=[42, 43]-=-. In the present case, reduction along the circle does not produce a geometry which is conformal to anti-de Sitter, and the reason is that the reduction being carried out is not along a spacelike circ... |

54 |
Differential regularization and renormalization: A New method of calculation in quantum field theory
- Freedman, Johnson, et al.
- 1992
(Show Context)
Citation Context ...nctions in conformal perturbation theory. Explicit expressions for the corrections to correlation functions at leading order in b were obtained in [16] using the method of differential regularization =-=[45]-=-. Counterterms in this method are implicit, although they can be constructed explicitly as in [46]. In the case at hand we would like to explore the structure of the required counterterms and compare ... |

46 |
Families of IIB duals for nonrelativistic CFTs
- Hartnoll, Yoshida
(Show Context)
Citation Context ...ctifications. In the case of z > 1, various embeddings into string theory have been found, with the massive vector actions arising as consistent truncations of type II supergravities, see for example =-=[6, 27, 28, 29, 30, 31, 32, 33, 34, 35]-=-. Note that in these cases the truncation to a graviton and massive vector suffices for the zero temperature background, but additional scalar fields are switched on in the corresponding black hole so... |

43 |
Supersymmetric solutions for non-relativistic holography
- Donos, Gauntlett
(Show Context)
Citation Context ...ctifications. In the case of z > 1, various embeddings into string theory have been found, with the massive vector actions arising as consistent truncations of type II supergravities, see for example =-=[6, 27, 28, 29, 30, 31, 32, 33, 34, 35]-=-. Note that in these cases the truncation to a graviton and massive vector suffices for the zero temperature background, but additional scalar fields are switched on in the corresponding black hole so... |

41 |
The geometry of Schródinger symmetry in gravity background/non-relativistic CFT,” Annals Phys
- Duval, Hassaine, et al.
- 2009
(Show Context)
Citation Context ...2xbVv. (1.4) 1An earlier approach to the geometric realization of non-relativistic symmetries can be found in [3] and the connection between this approach and holographic realizations is discussed in =-=[4]-=-. 3 With respect to the relativistic scaling dimension, this deformation is relevant for z < 1, marginal for z = 1 and irrelevant for z > 1. However, the deformation is exactly marginal with respect t... |

31 |
Holography for Schrodinger backgrounds,
- Guica, Skenderis, et al.
- 2011
(Show Context)
Citation Context ...ase of Schrödinger (z = 2) has been extensively studied in previous literature, but the encoding of the dual stress energy tensor in the asymptotics of the bulk geometry remains elusive. As shown in =-=[16]-=- there are several reasons for this subtlety. Firstly, the natural operator in the anisotropic dual theory couples not to the metric, but to the vielbein. Secondly, linearized sources for the dual str... |

28 | Dust as a standard of space and time in canonical quantum gravity
- Brown, Kuchař
- 1995
(Show Context)
Citation Context ...nsistent truncation found in [6]. It is interesting however to note that the black hole solution can be supported by dust or by a perfect fluid; appropriate actions for dust solutions can be found in =-=[52]-=- and for perfect fluids in [53]. Starting from (6.2), the normal to the hypersurfaces of constant r is null at the horizon as well as the Killing vector ∂η: ||dr||2 = 0 = ||∂η|| at r+. To see that the... |

26 |
Excitation Spectrum and Order Parameter for the Integrable N-State
- Albertini, McCoy, et al.
- 1989
(Show Context)
Citation Context ...odels admit a continuum limit at criticality which is described by two-dimensional ZN conformal field theories [11]. Since the chiral ZN models are inherently anisotropic in their critical properties =-=[12, 13, 14]-=-, they cannot be 2Whilst such theories are often called non-relativistic, or Schr(z), this terminology is arguably somewhat misleading; the theory only becomes non-relativistic after compactification ... |

24 | Classification of solutions in topologically massive gravity
- Chow, Pope, et al.
(Show Context)
Citation Context ...with generic z can be realized as solutions of TMG: the spacetime solves the TMG field equations when µ = (2z − 1). These TMG solutions were discussed in [17] and fit into the classification given in =-=[18]-=- as pp-waves. Solutions of this type with u compactified were recently discussed in [19]. In [20, 21] details of the holographic dictionary for TMG were presented, and this dictionary reflects the var... |

22 |
denNijs Quantum Model for Commensurate-Incommensurate Transitions Nucl. Phys. B215
- Howes, Kadanoff, et al.
- 1983
(Show Context)
Citation Context ...y model interesting physical systems and have appeared previously in the condensed matter literature. For example, the ZN chiral Potts models were introduced to model systems with melting transitions =-=[9, 10]-=-. The isotropic ZN models admit a continuum limit at criticality which is described by two-dimensional ZN conformal field theories [11]. Since the chiral ZN models are inherently anisotropic in their ... |

22 | Chiral deformations of conformal field theories
- Dijkgraaf
- 1997
(Show Context)
Citation Context ...olomorphic component of the stress energy tensor. Such chiral deformations of CFTs have arisen previously in many contexts, from two-dimensional large N QCD to Kodaira-Spencer theory, see for example =-=[44]-=-, but the existence and implications of the anisotropic scaling symmetry have not been discussed. From the form of (3.8) one can see that a theory with exponent z can also be viewed as a theory with e... |

20 |
Schrodinger invariant solutions of type IIB with enhanced supersymmetry
- Donos, Gauntlett
(Show Context)
Citation Context |

20 |
KK spectroscopy of type
- Ceresole, Dall’Agata, et al.
- 1999
(Show Context)
Citation Context ...dual to supergravity modes in Sasaki-Einstein compactifications are however generic. As an example, let us consider the T 1,1 compactification of type IIB supergravity, whose spectrum was computed in =-=[37, 38]-=-. Since T 1,1 is a rank one SU(2)2/U(1) coset, all differential operators can be expressed in terms of the Laplace-Beltrami operator, which is the only functionally independent differential operator. ... |

17 | Mass and angular momentum of asymptotically AdS or flat solutions in the topologically massive gravity - Olmez, Sarioglu, et al. - 2005 |

16 |
Compactification in the lightlike limit,” Phys
- Hellerman, Polchinski
- 1999
(Show Context)
Citation Context ... and one cannot trust the metric (1.1) with a compact null direction, see the discussions in [6]. (The problems in compactifying any field theory along a null direction are discussed in, for example, =-=[7]-=- and would in particular apply to the field theories considered here.) Recent work aiming at obtaining Schrödinger solutions without such a compact direction can be found in [8]. For general z and σ2... |

15 |
Microscopics of Extremal Kerr from Spinning M5 Branes,” [arXiv:1010.0685 [hep-th
- Compere, Song, et al.
(Show Context)
Citation Context ...nsional anisotropic systems such as those explored in [5]. Finally, let us comment on the relation between this work and recent attempts to understand the microscopics of the Kerr/CFT correspondence, =-=[54]-=- and [55]. In [54] a supergravity solution was considered which interpolates between a self-dual null orbifold of AdS3×S2 and the near-horizon limit of the extremal Kerr black hole times a circle, and... |

13 | Solutions of type IIB and D=11 supergravity with Schrodinger(z) symmetry
- Donos, Gauntlett
(Show Context)
Citation Context |

11 |
Free energy of the solvable chiral Potts model
- Baxter
- 1988
(Show Context)
Citation Context ...odels admit a continuum limit at criticality which is described by two-dimensional ZN conformal field theories [11]. Since the chiral ZN models are inherently anisotropic in their critical properties =-=[12, 13, 14]-=-, they cannot be 2Whilst such theories are often called non-relativistic, or Schr(z), this terminology is arguably somewhat misleading; the theory only becomes non-relativistic after compactification ... |

11 | AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence
- Skenderis, Taylor, et al.
(Show Context)
Citation Context ...when µ = (2z − 1). These TMG solutions were discussed in [17] and fit into the classification given in [18] as pp-waves. Solutions of this type with u compactified were recently discussed in [19]. In =-=[20, 21]-=- details of the holographic dictionary for TMG were presented, and this dictionary reflects the various problems of the theory: the theory is non-unitary and contains negative norm states. The most im... |

9 |
The superintegrable chiral Potts model, Phys. Letts. A 133
- Baxter
- 1988
(Show Context)
Citation Context ...odels admit a continuum limit at criticality which is described by two-dimensional ZN conformal field theories [11]. Since the chiral ZN models are inherently anisotropic in their critical properties =-=[12, 13, 14]-=-, they cannot be 2Whilst such theories are often called non-relativistic, or Schr(z), this terminology is arguably somewhat misleading; the theory only becomes non-relativistic after compactification ... |

8 |
Critical Exponents of the Chiral Potts Model from Conformal Field Theory, Nucl. Phys. B389
- Cardy
- 1993
(Show Context)
Citation Context ...or any z and in this paper we will explore holographic duality for these models. In the context of two dimensional conformal field theories, such deformations have been previously considered by Cardy =-=[5]-=- and the resulting models were called chiral scale-invariant models, a terminology which we will adopt here2. In the case of z = 2 the original goal was to model holographically a dual non-relativisti... |

7 |
A Cutoff procedure and counterterms for differential renormalization,” Nucl. Phys. B395
- Freedman, Johnson, et al.
- 1993
(Show Context)
Citation Context ...functions at leading order in b were obtained in [16] using the method of differential regularization [45]. Counterterms in this method are implicit, although they can be constructed explicitly as in =-=[46]-=-. In the case at hand we would like to explore the structure of the required counterterms and compare it with the counterterms obtained in holographic renormalization. Following [16], the leading orde... |

6 | The Particle number in Galilean holography
- Balasubramanian, McGreevy
(Show Context)
Citation Context ...ssed in, for example, [7] and would in particular apply to the field theories considered here.) Recent work aiming at obtaining Schrödinger solutions without such a compact direction can be found in =-=[8]-=-. For general z and σ2 > 0 one can reduce along u (for z < 1) and v (for z > 1) to obtain a (d − 1)-dimensional theory with non-relativistic scale invariance; in all cases the reduction is however nul... |

5 |
Incommensurate and commensurate phases in asymmetric clock models,
- Ostlund
- 1981
(Show Context)
Citation Context ...y model interesting physical systems and have appeared previously in the condensed matter literature. For example, the ZN chiral Potts models were introduced to model systems with melting transitions =-=[9, 10]-=-. The isotropic ZN models admit a continuum limit at criticality which is described by two-dimensional ZN conformal field theories [11]. Since the chiral ZN models are inherently anisotropic in their ... |

4 |
Holographic real-time non-relativistic correlators at zero and finite temperature, Phys.Rev. D82
- Barnes, Vaman, et al.
- 2010
(Show Context)
Citation Context ...hat for all z hypersurfaces of constant u are null. In the case of z > 1, the u coordinate has been treated as a time coordinate and real-time physics has been defined with respect to this coordinate =-=[24, 25]-=-. However, the fact hypersurfaces of constant u are actually null is symptomatic of a larger issue: there is no global time function in these spacetimes and the spacetimes are said to be causally non-... |

4 | Galilean Anti-De-Sitter Spacetime in Romans Theory,” Phys
- Singh
(Show Context)
Citation Context |

3 | The Curious Case of Null Warped Space
- Anninos, Compere, et al.
(Show Context)
Citation Context ...quations when µ = (2z − 1). These TMG solutions were discussed in [17] and fit into the classification given in [18] as pp-waves. Solutions of this type with u compactified were recently discussed in =-=[19]-=-. In [20, 21] details of the holographic dictionary for TMG were presented, and this dictionary reflects the various problems of the theory: the theory is non-unitary and contains negative norm states... |

3 | On variational principles for gravitating perfect fluids
- Brown
(Show Context)
Citation Context ...]. It is interesting however to note that the black hole solution can be supported by dust or by a perfect fluid; appropriate actions for dust solutions can be found in [52] and for perfect fluids in =-=[53]-=-. Starting from (6.2), the normal to the hypersurfaces of constant r is null at the horizon as well as the Killing vector ∂η: ||dr||2 = 0 = ||∂η|| at r+. To see that the Killing is normal to r = r+, o... |

2 |
String Dual of a Bose-Einstein Condensate,” arXiv:1009.0651 [hep-th
- Singh
(Show Context)
Citation Context |

1 |
Lifshitz-like systems and AdS null deformations,” arXiv:1103.1279 [hepth
- Narayan
(Show Context)
Citation Context ...roof will be discussed in the next section. 3After this paper was published, we became aware of related discussions of null scalar deformations in the earlier work [39]. See also the more recent work =-=[40]-=-. 13 This system is particularly interesting for the following reason. If one considers the case where dF = du, the metric can be written as ds2 = dρ2 4ρ2 + 1 ρ ( dxidx i − σ−2dv 2 ρ ) + σ2(du+ ρ−1σ−2... |