### Citations

3973 |
Handbook of Mathematical Functions
- Abramowitz, Stegun
- 1970
(Show Context)
Citation Context ...ne, i.e. ∆x+ ≪ ∆xi, the 2-pt function exhibits spatial power law behaviour 1[∑i(∆xi)2]∆ . In greater detail, the radial equation (9) is exactly solvable in terms of confluent hypergeometric functions =-=[48]-=-. Taking R(w) = w∆eαw 2 f(w), and redefining k2 = χ2 + k2i ≡ −2k+k− + k2i , α = − iQk− 2 , ∆ = 2 + √ 4 +m2 = 2 + ν, (10) the radial equation becomes z d 2f dz2 +(∆−1−z) df dz − (∆−1 2 − k2 8α )f = 0 (... |

343 | Lectures on holographic methods for condensed matter physics,” arXiv:0903.3246 [hep-th
- Hartnoll
(Show Context)
Citation Context ...t is interesting to explore generalizations of holographic duality to physical systems with nonrelativistic symmetries, with a view towards possible interfaces with condensed matter systems (see e.g. =-=[1, 2, 3]-=- for reviews). In this paper, we discuss Lifshitz-like fixed points from a holographic point of view. Lifshitz points arise in various condensed matter systems, e.g. magnetic systems with antiferromag... |

318 |
Evidence for F-Theory,” Nucl
- Vafa
- 1996
(Show Context)
Citation Context ...along the lines of non-geometric string constructions. Supergravity solutions involving nongeometric constructions with nontrivial winding around U-duality orbits have been studied previously in e.g. =-=[51, 52, 53, 54, 55]-=-. The S-duality in question here makes our construction nonperturbative, in contrast to some of these constructions that involve Tduality. However, the backgrounds in question here are considerably si... |

300 | Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry,” Phys - Son |

176 |
Comments on string theory backgrounds with non-relativistic conformal symmetry
- Maldacena, Martelli, et al.
(Show Context)
Citation Context ... → x+ − 12(2vixi − v2i x−), are broken by the g++ ∼ (Φ′)2 term. (If g++ = 0, this is essentially AdS in lightcone coordinates and the system upon DLCQ has a Schrodinger symmetry, as discussed in e.g. =-=[14, 15, 11]-=-). In the AdS5-deformed case, the gauge theory dual to these systems can be identified to be the DLCQ of the N=4 super Yang-Mills theory with a gauge coupling varying along the x+-direction as g2YM = ... |

169 |
Gravity Duals of Lifshitz-like Fixed
- Kachru, Liu, et al.
(Show Context)
Citation Context ...action S = ∫ dtd2x ((∂tϕ) 2 − κ(∇2ϕ)2). Aspects of correlation functions in these theories have been discussed in e.g. [6, 7]. Holographic dual gravitational models of such theories were described in =-=[8]-=-: these spacetimes ds2 = − dt2 r2z + dx2i+dr 2 r2 , i = 1, 2, arise as solutions to 4-dim Einstein gravity with a cosmological constant coupled to a massive abelian gauge field. The symmetries exhibit... |

155 |
Lectures on Holographic Superfluidity and Superconductivity
- Herzog
- 2009
(Show Context)
Citation Context ...t is interesting to explore generalizations of holographic duality to physical systems with nonrelativistic symmetries, with a view towards possible interfaces with condensed matter systems (see e.g. =-=[1, 2, 3]-=- for reviews). In this paper, we discuss Lifshitz-like fixed points from a holographic point of view. Lifshitz points arise in various condensed matter systems, e.g. magnetic systems with antiferromag... |

150 | Holographic duality with a view toward many-body physics,” arXiv:0909.0518
- McGreevy
(Show Context)
Citation Context ...t is interesting to explore generalizations of holographic duality to physical systems with nonrelativistic symmetries, with a view towards possible interfaces with condensed matter systems (see e.g. =-=[1, 2, 3]-=- for reviews). In this paper, we discuss Lifshitz-like fixed points from a holographic point of view. Lifshitz points arise in various condensed matter systems, e.g. magnetic systems with antiferromag... |

142 |
Principles of condensed matter physics
- Chaikin, Lubensky
- 1995
(Show Context)
Citation Context ...om a holographic point of view. Lifshitz points arise in various condensed matter systems, e.g. magnetic systems with antiferromagnetic interactions, dimer models, liquid crystals and so on (see e.g. =-=[4, 5]-=- for lucid descriptions). They exhibit the anisotropic scaling t → λzt, xi → λxi, with z the dynamical exponent. A Landau-Ginzburg description for such theories with z = 2 has the effective action S =... |

134 | Gravity duals for non-relativistic CFTs,” Phys - Balasubramanian, McGreevy - 2008 |

123 | Geometric Constructions of Nongeometric String Theories
- Hellerman, McGreevy, et al.
(Show Context)
Citation Context ...along the lines of non-geometric string constructions. Supergravity solutions involving nongeometric constructions with nontrivial winding around U-duality orbits have been studied previously in e.g. =-=[51, 52, 53, 54, 55]-=-. The S-duality in question here makes our construction nonperturbative, in contrast to some of these constructions that involve Tduality. However, the backgrounds in question here are considerably si... |

117 | Towards strange metallic holography,”
- Hartnoll, Polchinski, et al.
- 2010
(Show Context)
Citation Context ...pic scaling above: these are smaller than the Galilean symmetries explored holographically in [9]- [24]. Previous attempts at string or supergravity constructions of such spacetimes Lif4 include e.g. =-=[16, 25, 26, 27, 28, 29]-=-. In [30], certain lightlike deformations of AdS5 ×X5 sourced by a lightlike dilaton in Type IIB string theory (as well as those of AdS4 ×X7 in M-theory) were argued to give rise, upon dimensional red... |

114 | String theory
- Klebanov
(Show Context)
Citation Context ...2(k+ − iQ)k− ) ( k2i − 2(k+ + iQ)k− ) . (15) Thus the effective x+-momentum is shifted as k+ → k+ ± iQ, and eik+x+ → eik+x+e±Qx+. This is reminiscent of the Liouville-like wall in c = 1 string theory =-=[49, 50]-=-. Also note that for ki = 0, we have (k 2 i − 2k+k−)2 + 4Q2k2− → (k2+ + Q2)k2−, which gives an effective mass-gap in the x+-direction. Another corroboration of this interpretation comes from looking a... |

104 | Heating up Galilean holography - Herzog, Rangamani, et al. |

104 |
Non-relativistic holography,” [arXiv:0812.0530 [hep-th
- Taylor
(Show Context)
Citation Context ...pic scaling above: these are smaller than the Galilean symmetries explored holographically in [9]- [24]. Previous attempts at string or supergravity constructions of such spacetimes Lif4 include e.g. =-=[16, 25, 26, 27, 28, 29]-=-. In [30], certain lightlike deformations of AdS5 ×X5 sourced by a lightlike dilaton in Type IIB string theory (as well as those of AdS4 ×X7 in M-theory) were argued to give rise, upon dimensional red... |

99 |
Scaling and Renormalization in Statistical Physics
- Cardy
- 1996
(Show Context)
Citation Context ...om a holographic point of view. Lifshitz points arise in various condensed matter systems, e.g. magnetic systems with antiferromagnetic interactions, dimer models, liquid crystals and so on (see e.g. =-=[4, 5]-=- for lucid descriptions). They exhibit the anisotropic scaling t → λzt, xi → λxi, with z the dynamical exponent. A Landau-Ginzburg description for such theories with z = 2 has the effective action S =... |

91 | Duality twists, orbifolds, and fluxes
- Dabholkar, Hull
(Show Context)
Citation Context ...along the lines of non-geometric string constructions. Supergravity solutions involving nongeometric constructions with nontrivial winding around U-duality orbits have been studied previously in e.g. =-=[51, 52, 53, 54, 55]-=-. The S-duality in question here makes our construction nonperturbative, in contrast to some of these constructions that involve Tduality. However, the backgrounds in question here are considerably si... |

72 |
Orbital theory,
- Benjamin
- 1965
(Show Context)
Citation Context ...pic scaling above: these are smaller than the Galilean symmetries explored holographically in [9]- [24]. Previous attempts at string or supergravity constructions of such spacetimes Lif4 include e.g. =-=[16, 25, 26, 27, 28, 29]-=-. In [30], certain lightlike deformations of AdS5 ×X5 sourced by a lightlike dilaton in Type IIB string theory (as well as those of AdS4 ×X7 in M-theory) were argued to give rise, upon dimensional red... |

70 |
AdS/CFT duality for non-relativistic field theory
- Goldberger
(Show Context)
Citation Context ... → x+ − 12(2vixi − v2i x−), are broken by the g++ ∼ (Φ′)2 term. (If g++ = 0, this is essentially AdS in lightcone coordinates and the system upon DLCQ has a Schrodinger symmetry, as discussed in e.g. =-=[14, 15, 11]-=-). In the AdS5-deformed case, the gauge theory dual to these systems can be identified to be the DLCQ of the N=4 super Yang-Mills theory with a gauge coupling varying along the x+-direction as g2YM = ... |

70 |
Lifshitz spacetimes from AdS null and cosmological solutions,
- Balasubramanian, Narayan
- 2010
(Show Context)
Citation Context ...smaller than the Galilean symmetries explored holographically in [9]- [24]. Previous attempts at string or supergravity constructions of such spacetimes Lif4 include e.g. [16, 25, 26, 27, 28, 29]. In =-=[30]-=-, certain lightlike deformations of AdS5 ×X5 sourced by a lightlike dilaton in Type IIB string theory (as well as those of AdS4 ×X7 in M-theory) were argued to give rise, upon dimensional reduction, t... |

52 |
Constructing Lifshitz solutions from AdS,
- Cassani, Faedo
- 2011
(Show Context)
Citation Context ...of similar z = 2 solutions with various other fields incorporated. Lifshitz-like solutions with more general values of the dynamical exponent z have been constructed in [32] (see also related work in =-=[33, 34, 35, 36, 37, 38]-=-). 1 In this paper, we continue to explore the apparently simpler systems in [30], but now without any compactification. This is a lightlike deformation of AdS5 ×X5 sourced by a null dilaton, dual to ... |

46 | Families of IIB duals for nonrelativistic CFTs - Hartnoll, Yoshida |

44 |
On Existence of Self-Tuning Solutions
- Koroteev, Libanov
- 2008
(Show Context)
Citation Context |

43 | Supersymmetric solutions for non-relativistic holography - Donos, Gauntlett |

42 |
Topological order and conformal quantum critical points,” Annals Phys
- Ardonne, Fendley, et al.
- 2004
(Show Context)
Citation Context ...nt. A Landau-Ginzburg description for such theories with z = 2 has the effective action S = ∫ dtd2x ((∂tϕ) 2 − κ(∇2ϕ)2). Aspects of correlation functions in these theories have been discussed in e.g. =-=[6, 7]-=-. Holographic dual gravitational models of such theories were described in [8]: these spacetimes ds2 = − dt2 r2z + dx2i+dr 2 r2 , i = 1, 2, arise as solutions to 4-dim Einstein gravity with a cosmolog... |

39 | On the spectrum of nonrelativistic AdS/CFT
- Barbon, Fuertes
(Show Context)
Citation Context ... → x+ − 12(2vixi − v2i x−), are broken by the g++ ∼ (Φ′)2 term. (If g++ = 0, this is essentially AdS in lightcone coordinates and the system upon DLCQ has a Schrodinger symmetry, as discussed in e.g. =-=[14, 15, 11]-=-). In the AdS5-deformed case, the gauge theory dual to these systems can be identified to be the DLCQ of the N=4 super Yang-Mills theory with a gauge coupling varying along the x+-direction as g2YM = ... |

39 |
Lectures on 2-D gravity and 2-D string theory,” arXiv:hep-th/9304011
- Ginsparg, Moore
(Show Context)
Citation Context ...2(k+ − iQ)k− ) ( k2i − 2(k+ + iQ)k− ) . (15) Thus the effective x+-momentum is shifted as k+ → k+ ± iQ, and eik+x+ → eik+x+e±Qx+. This is reminiscent of the Liouville-like wall in c = 1 string theory =-=[49, 50]-=-. Also note that for ki = 0, we have (k 2 i − 2k+k−)2 + 4Q2k2− → (k2+ + Q2)k2−, which gives an effective mass-gap in the x+-direction. Another corroboration of this interpretation comes from looking a... |

28 |
Some No-go Theorems for String Duals of Non-relativistic Lifshitz-like Theories
- Li, Nishioka, et al.
- 2009
(Show Context)
Citation Context |

25 |
Time dependent cosmologies and their duals, Phys. Rev
- Das, Michelson, et al.
(Show Context)
Citation Context ...y− + dx2i ) + dr2] + dΩ25, Φ = Φ(x+) , (2) with the 4-dim part being conformal to flat space, the boundary metric becoming efηµν : indeed this is where the AdS5-deformed systems were originally found =-=[41, 42, 43, 44]-=- (see also [45, 46]) 1. These are Penrose-Brown-Henneaux (PBH) transformations, a subset of bulk diffeomorphisms leaving the metric invariant (in Fefferman-Graham form), and acting as a Weyl transform... |

22 | Holography of charged dilaton black holes,”
- Goldstein, Kachru, et al.
- 2010
(Show Context)
Citation Context ...ane and z = ∞ scaling for the x+, x−- directions. This is reminiscent of the anisotropic scaling2 observed in the D3-D7 construction of [28] and the scalings in the dilatonic black brane solutions in =-=[40]-=-: however in this case, the scaling (5) is an actual symmetry of (4), respected by the dilaton Φ(x+) as well. This sort of 2We recall that radial Kasner-like solutions of the form ds2 = 1 r2 [dr2− r2p... |

21 | Special limits and non-relativistic solutions
- Singh
(Show Context)
Citation Context ...of similar z = 2 solutions with various other fields incorporated. Lifshitz-like solutions with more general values of the dynamical exponent z have been constructed in [32] (see also related work in =-=[33, 34, 35, 36, 37, 38]-=-). 1 In this paper, we continue to explore the apparently simpler systems in [30], but now without any compactification. This is a lightlike deformation of AdS5 ×X5 sourced by a null dilaton, dual to ... |

21 | Holography for chiral scale-invariant models,
- Costa, Taylor
- 2011
(Show Context)
Citation Context ...of similar z = 2 solutions with various other fields incorporated. Lifshitz-like solutions with more general values of the dynamical exponent z have been constructed in [32] (see also related work in =-=[33, 34, 35, 36, 37, 38]-=-). 1 In this paper, we continue to explore the apparently simpler systems in [30], but now without any compactification. This is a lightlike deformation of AdS5 ×X5 sourced by a null dilaton, dual to ... |

20 |
Schrodinger invariant solutions of type IIB with enhanced supersymmetry
- Donos, Gauntlett
(Show Context)
Citation Context ...ited by this spacetime are time translations, spatial translations/rotations, as well as the anisotropic scaling above: these are smaller than the Galilean symmetries explored holographically in [9]- =-=[24]-=-. Previous attempts at string or supergravity constructions of such spacetimes Lif4 include e.g. [16, 25, 26, 27, 28, 29]. In [30], certain lightlike deformations of AdS5 ×X5 sourced by a lightlike di... |

18 | Supersymmetric non-relativistic geometries in M-theory - Ooguri, Park |

18 |
Vacua of M-theory and string theory,” Phys
- Kallosh, Rajaraman
- 1998
(Show Context)
Citation Context ...o the lightlike nature of these solutions, which suggests that higher derivative corrections to the solution in fact vanish, i.e. that these are exact string backgrounds (perhaps similar to AdS5 × S5 =-=[56]-=-). We have seen that a way to uplift the Lifshitz-like symmetries of the 4-dim Lifshitz system to the 5-dim system is to turn on lightlike deformations of the form (17) which reflect these Lifshitz-li... |

12 | Gauge Theory Duals of Cosmological Backgrounds and their Energy Momentum Tensors, Phys. Rev. D77
- Awad, Das, et al.
- 2008
(Show Context)
Citation Context ...y− + dx2i ) + dr2] + dΩ25, Φ = Φ(x+) , (2) with the 4-dim part being conformal to flat space, the boundary metric becoming efηµν : indeed this is where the AdS5-deformed systems were originally found =-=[41, 42, 43, 44]-=- (see also [45, 46]) 1. These are Penrose-Brown-Henneaux (PBH) transformations, a subset of bulk diffeomorphisms leaving the metric invariant (in Fefferman-Graham form), and acting as a Weyl transform... |

11 |
Cosmologies with null singularities and their gauge theory duals
- Das, Michelson, et al.
(Show Context)
Citation Context ...y− + dx2i ) + dr2] + dΩ25, Φ = Φ(x+) , (2) with the 4-dim part being conformal to flat space, the boundary metric becoming efηµν : indeed this is where the AdS5-deformed systems were originally found =-=[41, 42, 43, 44]-=- (see also [45, 46]) 1. These are Penrose-Brown-Henneaux (PBH) transformations, a subset of bulk diffeomorphisms leaving the metric invariant (in Fefferman-Graham form), and acting as a Weyl transform... |

10 | Non-relativistic M-Theory solutions based - Colgain, Varela, et al. |

10 | Riet, “Lifshitz backgrounds from 10d supergravity
- Blaback, Danielsson, et al.
(Show Context)
Citation Context |

9 |
Finite temperature properties of quantum Lifshitz transitions between valence bond solid phases: An expamle of ‘local’ quantum criticality,” Phys
- Ghaemi, Vishwanath, et al.
(Show Context)
Citation Context ...nt. A Landau-Ginzburg description for such theories with z = 2 has the effective action S = ∫ dtd2x ((∂tϕ) 2 − κ(∇2ϕ)2). Aspects of correlation functions in these theories have been discussed in e.g. =-=[6, 7]-=-. Holographic dual gravitational models of such theories were described in [8]: these spacetimes ds2 = − dt2 r2z + dx2i+dr 2 r2 , i = 1, 2, arise as solutions to 4-dim Einstein gravity with a cosmolog... |

6 |
Electric / magnetic deformations of S**3 and AdS(3), and geometric cosets,” Fortsch. Phys. 53, 73 (2005) [arXiv:hep-th/0405213]; see also
- Israel, Kounnas, et al.
(Show Context)
Citation Context ...wn to preserve half (lightcone) supersymmetry in the 1After this paper appeared on the arXiv, we were informed of earlier solutions representing null deformations of AdS3 in the context of WZW models =-=[47]-=-. 3 form (2) in [41]. Supersymmetry was also shown for various solutions in the more general family in [31] which are generalizations of the metric form (1). An argument for the dimensional reduction ... |

3 |
Gauge Theories with Time Dependent
- Awad, Das, et al.
(Show Context)
Citation Context |

2 | One-loop effect of null-like cosmology’s holographic dual JHEP 0703
- Lin, Wen
- 2007
(Show Context)
Citation Context ...Φ = Φ(x+) , (2) with the 4-dim part being conformal to flat space, the boundary metric becoming efηµν : indeed this is where the AdS5-deformed systems were originally found [41, 42, 43, 44] (see also =-=[45, 46]-=-) 1. These are Penrose-Brown-Henneaux (PBH) transformations, a subset of bulk diffeomorphisms leaving the metric invariant (in Fefferman-Graham form), and acting as a Weyl transformation on the bounda... |

1 |
JHEP 0604, 013 (2006) [arXiv:hep-th/0602054
- Chu, Ho
(Show Context)
Citation Context ...Φ = Φ(x+) , (2) with the 4-dim part being conformal to flat space, the boundary metric becoming efηµν : indeed this is where the AdS5-deformed systems were originally found [41, 42, 43, 44] (see also =-=[45, 46]-=-) 1. These are Penrose-Brown-Henneaux (PBH) transformations, a subset of bulk diffeomorphisms leaving the metric invariant (in Fefferman-Graham form), and acting as a Weyl transformation on the bounda... |