### Citations

5599 | The Large N limit of superconformal field theories and supergravity,” Adv.Theor.Math.Phys
- Maldacena
- 1998
(Show Context)
Citation Context .... 12 4 Holographic entanglement entropy 16 5 Discussion 19 1 Introduction Various fascinating explorations of strongly coupled quantum field theories have been carried out using gauge/gravity duality =-=[1]-=-, including, more recently, non-relativistic and condensed matter systems [2] with symmetries typically smaller than anti de Sitter space. Several interesting features of finite density systems can in... |

615 |
Central charges in the canonical realization of asymptotic symmetries: An example from three-dimensional gravity
- Brown, Henneaux
- 1986
(Show Context)
Citation Context ...aking some general comments here. As discussed in [40], the coordinate transformations above, recasting the metric to have a conformally flat boundary, are PenroseBrown-Henneaux (PBH) transformations =-=[47, 48, 49, 50, 51]-=-: these are bulk diffeomorphisms acting as a Weyl transformation on the boundary. In general, a PBH transformation changes the bulk foliation and thus the near-boundary Fefferman-Graham expansion. In ... |

527 |
A Stress tensor for Anti-de Sitter gravity, Commun.Math.Phys
- Balasubramanian, Kraus
- 1999
(Show Context)
Citation Context ... dr2 r2 + hµνdx µdxν = dr2 r2 + 1 r2 (g(0)µν + r 2g(2)µν + r 4g(4)µν + . . .)dx µdxν , (5) written in the Fefferman-Graham expansion about the boundary r = 0. Then holographic renormalization methods =-=[32, 33, 34, 35, 36]-=- give relations between the metric coefficients g (k) µν and the holographic stress tensor calculated as Tµν ∼ limr→0 1r2 1G5 (Kµν −Khµν − 3hµν), whereKµν is the extrinsic curvature 1. For (2), the on... |

453 |
Holographic reconstruction of spacetime and renormalization
- Haro, Solodukhin, et al.
(Show Context)
Citation Context ... dr2 r2 + hµνdx µdxν = dr2 r2 + 1 r2 (g(0)µν + r 2g(2)µν + r 4g(4)µν + . . .)dx µdxν , (5) written in the Fefferman-Graham expansion about the boundary r = 0. Then holographic renormalization methods =-=[32, 33, 34, 35, 36]-=- give relations between the metric coefficients g (k) µν and the holographic stress tensor calculated as Tµν ∼ limr→0 1r2 1G5 (Kµν −Khµν − 3hµν), whereKµν is the extrinsic curvature 1. For (2), the on... |

399 |
The holographic Weyl anomaly
- Henningson, Skenderis
- 1998
(Show Context)
Citation Context ...aking some general comments here. As discussed in [40], the coordinate transformations above, recasting the metric to have a conformally flat boundary, are PenroseBrown-Henneaux (PBH) transformations =-=[47, 48, 49, 50, 51]-=-: these are bulk diffeomorphisms acting as a Weyl transformation on the boundary. In general, a PBH transformation changes the bulk foliation and thus the near-boundary Fefferman-Graham expansion. In ... |

368 |
Holographic derivation of entanglement entropy from AdS/CFT,” Phys
- Ryu, Takayanagi
(Show Context)
Citation Context ...ded in the conformal factor: these have been discussed in e.g. [8, 9] motivating and clarifying connections with condensed matter systems (in particular pertaining to holographic entanglement entropy =-=[10]-=- and Fermi surfaces): see also [11] for various aspects of holography in this context. Some of these hyperscaling violating metrics can be realized by x+-dimensional reduction of metrics (1) using nor... |

280 |
Lecture notes on holographic renormalization
- Skenderis
- 2002
(Show Context)
Citation Context ... dr2 r2 + hµνdx µdxν = dr2 r2 + 1 r2 (g(0)µν + r 2g(2)µν + r 4g(4)µν + . . .)dx µdxν , (5) written in the Fefferman-Graham expansion about the boundary r = 0. Then holographic renormalization methods =-=[32, 33, 34, 35, 36]-=- give relations between the metric coefficients g (k) µν and the holographic stress tensor calculated as Tµν ∼ limr→0 1r2 1G5 (Kµν −Khµν − 3hµν), whereKµν is the extrinsic curvature 1. For (2), the on... |

176 |
Comments on string theory backgrounds with non-relativistic conformal symmetry
- Maldacena, Martelli, et al.
(Show Context)
Citation Context ... the homogenous case. It would be interesting to understand this better, including finite temperature versions. In this regard, it is useful to recall that boosted black branes in lightcone variables =-=[57]-=- in a certain zero-temperature double scaling limit reduce to the homogenous AdS plane wave, as discussed in [14]. To elaborate, we see that the familiar black D3-branes ds2 = 1 r2 [−(1− r40r4)dt2 + d... |

169 |
Gravity Duals of Lifshitz-like Fixed
- Kachru, Liu, et al.
(Show Context)
Citation Context ...f the form ds2 = 1 r2 [−2dx+dx− + dx2i + dr2] + g++(dx+)2 + dΩ2S , (1) where the metric component g++ might be sourced by various fields. For instance, spacetimes with z = 2 Lifshitz scaling symmetry =-=[3, 4]-=- can be realized in string constructions via dimensional reduction along the x+-direction of metrics (1) with non-normalizable deformations g++ ∼ 1r2 r2 [5, 6] (see also e.g. [7]). Likewise, metrics c... |

145 |
Effective holographic theories for low-temperature condensed matter systems,”
- Charmousis, Gouteraux, et al.
- 2010
(Show Context)
Citation Context ...ealized by x+-dimensional reduction of metrics (1) using normalizable deformations g++ ∼ 1r2 r4 [12] (see also e.g. [11, 13, 14, 15, 16, 17, 18] for other string realizations of such models, and e.g. =-=[19, 20, 21, 22, 23, 24, 25, 26, 27]-=- for effective gravity models with vectors and scalars where these and related metrics arise, with associated physics). In particular, the AdS5 normalizable null deformation after dimensional 1 reduct... |

142 |
Bulk vs. boundary dynamics in anti-de Sitter spacetime,” Phys
- Balasubramanian, Kraus, et al.
- 1999
(Show Context)
Citation Context ...f4(xi) (6). In other words, a general spatially varying T++ maps to a (static) bulk dual metric with g++ as above. To put the current discussion in perspective with that on normalizable modes in e.g. =-=[37]-=-, consider a massless scalar field ϕ inAdS5 in lightcone coordinates: then 1√−g∂µ(g µν √−g∂νϕ) = 0 for modes ϕ = eik+x ++ik−x−+ikixiR(r) simplifies to R′′ − 3 r R′ − k2R = 0 , k2 ≡ kµkµ = −2k+k− + k2i... |

117 | Towards strange metallic holography,”
- Hartnoll, Polchinski, et al.
- 2010
(Show Context)
Citation Context ... scattering due to the “stuff” making up the sources, rendering the metric contribution alone likely incomplete: this has been discussed in [53] in the context of the Lifshitz string constructions in =-=[54]-=-. In this light, the Lifshitz backgrounds above are also likely to be good string backgrounds, even if they appear constrained from an AdS/CFT point of view at the level of supergravity (see also [55]... |

104 |
Non-relativistic holography,” [arXiv:0812.0530 [hep-th
- Taylor
(Show Context)
Citation Context ...f the form ds2 = 1 r2 [−2dx+dx− + dx2i + dr2] + g++(dx+)2 + dΩ2S , (1) where the metric component g++ might be sourced by various fields. For instance, spacetimes with z = 2 Lifshitz scaling symmetry =-=[3, 4]-=- can be realized in string constructions via dimensional reduction along the x+-direction of metrics (1) with non-normalizable deformations g++ ∼ 1r2 r2 [5, 6] (see also e.g. [7]). Likewise, metrics c... |

100 |
Hidden Fermi surfaces in compressible states of gauge-gravity duality,”
- Huijse, Sachdev, et al.
- 2012
(Show Context)
Citation Context ...]). Likewise, metrics conformal to Lifshitz spacetimes arise in holographic systems with nontrivial hyperscaling violation exponents encoded in the conformal factor: these have been discussed in e.g. =-=[8, 9]-=- motivating and clarifying connections with condensed matter systems (in particular pertaining to holographic entanglement entropy [10] and Fermi surfaces): see also [11] for various aspects of hologr... |

74 |
Aspects of holography for theories with hyperscaling violation,
- Dong, Harrison, et al.
- 2012
(Show Context)
Citation Context ...have been discussed in e.g. [8, 9] motivating and clarifying connections with condensed matter systems (in particular pertaining to holographic entanglement entropy [10] and Fermi surfaces): see also =-=[11]-=- for various aspects of holography in this context. Some of these hyperscaling violating metrics can be realized by x+-dimensional reduction of metrics (1) using normalizable deformations g++ ∼ 1r2 r4... |

72 |
Generalized holographic quantum criticality at finite density,
- Gouteraux, Kiritsis
- 2011
(Show Context)
Citation Context ...ealized by x+-dimensional reduction of metrics (1) using normalizable deformations g++ ∼ 1r2 r4 [12] (see also e.g. [11, 13, 14, 15, 16, 17, 18] for other string realizations of such models, and e.g. =-=[19, 20, 21, 22, 23, 24, 25, 26, 27]-=- for effective gravity models with vectors and scalars where these and related metrics arise, with associated physics). In particular, the AdS5 normalizable null deformation after dimensional 1 reduct... |

70 |
Lifshitz spacetimes from AdS null and cosmological solutions,
- Balasubramanian, Narayan
- 2010
(Show Context)
Citation Context ...mes with z = 2 Lifshitz scaling symmetry [3, 4] can be realized in string constructions via dimensional reduction along the x+-direction of metrics (1) with non-normalizable deformations g++ ∼ 1r2 r2 =-=[5, 6]-=- (see also e.g. [7]). Likewise, metrics conformal to Lifshitz spacetimes arise in holographic systems with nontrivial hyperscaling violation exponents encoded in the conformal factor: these have been ... |

64 |
Surface terms as counterterms in the AdS/CFT correspondence,” Phys
- Emparan, Johnson, et al.
- 1999
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52 | Constructing Lifshitz solutions from AdS, - Cassani, Faedo - 2011 |

51 |
Holographic Entanglement Entropy
- Boer, Kulaxizi, et al.
(Show Context)
Citation Context ...of holography in this context. Some of these hyperscaling violating metrics can be realized by x+-dimensional reduction of metrics (1) using normalizable deformations g++ ∼ 1r2 r4 [12] (see also e.g. =-=[11, 13, 14, 15, 16, 17, 18]-=- for other string realizations of such models, and e.g. [19, 20, 21, 22, 23, 24, 25, 26, 27] for effective gravity models with vectors and scalars where these and related metrics arise, with associate... |

51 |
Diffeomorphisms and holographic anomalies.
- Imbimbo, Schwimmer, et al.
- 2000
(Show Context)
Citation Context ...aking some general comments here. As discussed in [40], the coordinate transformations above, recasting the metric to have a conformally flat boundary, are PenroseBrown-Henneaux (PBH) transformations =-=[47, 48, 49, 50, 51]-=-: these are bulk diffeomorphisms acting as a Weyl transformation on the boundary. In general, a PBH transformation changes the bulk foliation and thus the near-boundary Fefferman-Graham expansion. In ... |

49 |
Stress tensors and Casimir energies in the AdS/CFT correspondence,” Phys
- Myers
- 1999
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43 |
Holographic striped phases
- Donos, Gauntlett
- 2011
(Show Context)
Citation Context ... for e.g. charged 4-dim AdS black brane solutions, so one might imagine technical similarities between the two systems in the analysis of linearized gravity perturbations, discussed for the latter in =-=[56]-=-. In the Lifshitz context, the massive gauge field and metric lift in the 5-dim metric-dilaton system to metric modes, and we can then look for perturbations restricting to simply normalizable metric ... |

42 | Holography for asymptotically locally Lifshitz spacetimes - Ross |

38 |
On Lifshitz scaling and hyperscaling violation in string theory,
- Narayan
- 2012
(Show Context)
Citation Context ...for various aspects of holography in this context. Some of these hyperscaling violating metrics can be realized by x+-dimensional reduction of metrics (1) using normalizable deformations g++ ∼ 1r2 r4 =-=[12]-=- (see also e.g. [11, 13, 14, 15, 16, 17, 18] for other string realizations of such models, and e.g. [19, 20, 21, 22, 23, 24, 25, 26, 27] for effective gravity models with vectors and scalars where the... |

33 | Domain Wall Holography for Finite Temperature Scaling Solutions
- Perlmutter
(Show Context)
Citation Context ...ealized by x+-dimensional reduction of metrics (1) using normalizable deformations g++ ∼ 1r2 r4 [12] (see also e.g. [11, 13, 14, 15, 16, 17, 18] for other string realizations of such models, and e.g. =-=[19, 20, 21, 22, 23, 24, 25, 26, 27]-=- for effective gravity models with vectors and scalars where these and related metrics arise, with associated physics). In particular, the AdS5 normalizable null deformation after dimensional 1 reduct... |

32 |
Phase transitions between ReissnerNordstrom and dilatonic black holes
- Cadoni, D’Appollonio, et al.
- 2010
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31 |
Spatially modulated instabilities of magnetic black branes
- Donos, Gauntlett, et al.
(Show Context)
Citation Context ...formations for the AdS5 case, these generically correspond in the dual field theory to SYM states with lightcone momentum density T++ varying spatially, the homogenous case studied in arXiv:1202.5935 =-=[hep-th]-=- corresponding to uniform T++. All of these preserve some supersymmetry. Generically these inhomogenous solutions exhibit analogs of horizons in the interior where a timelike Killing vector becomes nu... |

29 | Lifshitz/Schrodinger Dp-branes and dynamical exponents,
- Singh
- 2012
(Show Context)
Citation Context ...of holography in this context. Some of these hyperscaling violating metrics can be realized by x+-dimensional reduction of metrics (1) using normalizable deformations g++ ∼ 1r2 r4 [12] (see also e.g. =-=[11, 13, 14, 15, 16, 17, 18]-=- for other string realizations of such models, and e.g. [19, 20, 21, 22, 23, 24, 25, 26, 27] for effective gravity models with vectors and scalars where these and related metrics arise, with associate... |

25 | Schrodinger holography with and without hyperscaling violation,” - Kim - 2012 |

25 |
Time dependent cosmologies and their duals, Phys. Rev
- Das, Michelson, et al.
(Show Context)
Citation Context ...he general family of solutions ds2 = 1 r2 (g̃µν(x µ)dxµdxν + dr2) + dΩ25 , Φ = Φ(x µ) , (26) (after relabelling w as r) with the X5 and 5-form suppressed, and the conditions R̃µν = 1 2 ∂µΦ∂νΦ, Φ = 0 =-=[45, 40]-=- arising from the IIB supergravity equations of motion. These conditions can also be obtained using holographic renormalization methods [35, 36] and requiring that all subleading coefficients vanish f... |

24 |
Lifshitz-like space-time from intersecting branes in string/M theory,
- Dey, Roy
- 2012
(Show Context)
Citation Context ...of holography in this context. Some of these hyperscaling violating metrics can be realized by x+-dimensional reduction of metrics (1) using normalizable deformations g++ ∼ 1r2 r4 [12] (see also e.g. =-=[11, 13, 14, 15, 16, 17, 18]-=- for other string realizations of such models, and e.g. [19, 20, 21, 22, 23, 24, 25, 26, 27] for effective gravity models with vectors and scalars where these and related metrics arise, with associate... |

23 |
Non-Abelian T-duality and consistent truncations in type-II supergravity,
- Itsios, Lozano, et al.
- 2012
(Show Context)
Citation Context ... in this case. All normalizable g++ solutions have g++ →r→0 r2f4(xi) so their radial dependence near the boundary is similar to the homogenous AdS plane wave 2It is worth noting constructions such as =-=[39]-=- which may be useful in generating new solutions of this sort, perhaps with reduced supersymmetry. 10 case: near r → 0, the lower dimensional description (19) approaches ds24 = − dt2 r5 √ f4(xi) + √ f... |

22 | Holography of charged dilaton black holes,”
- Goldstein, Kachru, et al.
- 2010
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21 |
Thermal behavior of charged dilatonic black branes
- Bertoldi, Burrington, et al.
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21 | Holography for chiral scale-invariant models,
- Costa, Taylor
- 2011
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Citation Context ...es to r 2g′′++ + 3rg′++ = 0, which gives g++ = const as the normalizable solution, which is automatically homogenous (aspects of null or chiral deformations of conformal field theories appear in e.g. =-=[38]-=-). In general, these null deformations amount to turning on nontrivial expectation values for lightcone momentum density T++ in the dual conformal field theory: for M2- and M5branes, these AdS4×X7 and... |

20 | Bianchi attractors: a classification of extremal black brane geometries,
- Iizuka
- 2012
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18 |
Vacua of M-theory and string theory,” Phys
- Kallosh, Rajaraman
- 1998
(Show Context)
Citation Context ...alogs of plane-waves with possible inhomogeneities (see e.g. [28] for a recent review discussing plane-wave backgrounds [29] in the context of cosmological singularities). Since AdS5 × S5 is α′-exact =-=[30]-=- as are plane wave spacetimes, these AdS null deformations are also likely α′-exact string backgrounds. We will restrict in particular to static AdS deformations that are normalizable near the boundar... |

17 | Hyperscaling violation from supergravity,
- Perlmutter
- 2012
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17 | Lifshitz-like black brane thermodynamics in higher dimensions,
- Bertoldi, Burrington, et al.
- 2011
(Show Context)
Citation Context ...formations for the AdS5 case, these generically correspond in the dual field theory to SYM states with lightcone momentum density T++ varying spatially, the homogenous case studied in arXiv:1202.5935 =-=[hep-th]-=- corresponding to uniform T++. All of these preserve some supersymmetry. Generically these inhomogenous solutions exhibit analogs of horizons in the interior where a timelike Killing vector becomes nu... |

16 |
Lifshitz solutions in supergravity and string theory,
- Gregory, Parameswaran, et al.
- 2010
(Show Context)
Citation Context ...z scaling symmetry [3, 4] can be realized in string constructions via dimensional reduction along the x+-direction of metrics (1) with non-normalizable deformations g++ ∼ 1r2 r2 [5, 6] (see also e.g. =-=[7]-=-). Likewise, metrics conformal to Lifshitz spacetimes arise in holographic systems with nontrivial hyperscaling violation exponents encoded in the conformal factor: these have been discussed in e.g. [... |

15 | Holographic Renormalization for z=2 Lifshitz Space-Times from AdS”,
- Chemissany, Geissbuhler, et al.
- 2012
(Show Context)
Citation Context ...c and scalar vanishing. These conditions on the gnµν , Φ n, n > 0, are non-generic and appear to be nontrivial constraints fine-tuning the CFT state after turning on the sources g(0), Φ(0). 3See e.g. =-=[41, 42, 43, 44]-=- for recent discussions of holographic renormalization in Lifshitz backgrounds; see also [38]. 13 These arguments have also been discussed in [46] in the cosmological singularities context of [45, 40]... |

14 |
Space-Time Singularities in String Theory,” Phys
- Horowitz, Steif
- 1990
(Show Context)
Citation Context ...g++ having spatial (xi) dependence. These are near horizon limits of D3-brane analogs of plane-waves with possible inhomogeneities (see e.g. [28] for a recent review discussing plane-wave backgrounds =-=[29]-=- in the context of cosmological singularities). Since AdS5 × S5 is α′-exact [30] as are plane wave spacetimes, these AdS null deformations are also likely α′-exact string backgrounds. We will restrict... |

13 | Flows involving Lifshitz solutions,
- Braviner, Gregory, et al.
- 2011
(Show Context)
Citation Context ...c and scalar vanishing. These conditions on the gnµν , Φ n, n > 0, are non-generic and appear to be nontrivial constraints fine-tuning the CFT state after turning on the sources g(0), Φ(0). 3See e.g. =-=[41, 42, 43, 44]-=- for recent discussions of holographic renormalization in Lifshitz backgrounds; see also [38]. 13 These arguments have also been discussed in [46] in the cosmological singularities context of [45, 40]... |

12 | Gauge Theory Duals of Cosmological Backgrounds and their Energy Momentum Tensors, Phys. Rev. D77
- Awad, Das, et al.
- 2008
(Show Context)
Citation Context ...r fields (e.g. a null dilaton) sourcing the null deformation. To elaborate, consider first the case [5] where F (x+) is sourced by a lightlike scalar (e.g. the dilaton): then the stress tensor, using =-=[40]-=-, is Tµν ∼ 1 G5 ( Kµν −Khµν − 3hµν + 1 2 Gµν − 1 4 ∂µΦ∂νΦ + 1 8 hµν(∂Φ) 2 ) , (24) 12 where Gµν , ∂ here are defined w.r.t. the boundary metric hµν , and the scalar terms arise from counterterms invol... |

9 |
On holography with hyperscaling violation,”
- Alishahiha, Yavartanoo
- 2012
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9 |
Resolving Lifshitz Horizons,” arXiv:1202.6635 [hep-th
- Harrison, Kachru, et al.
(Show Context)
Citation Context ...[54]. In this light, the Lifshitz backgrounds above are also likely to be good string backgrounds, even if they appear constrained from an AdS/CFT point of view at the level of supergravity (see also =-=[55]-=- for other related discussions on Lifshitz singularities). For instance, in the case [5] where F (x+) ∼ (∂+Φ)2 is sourced by a lightlike dilaton Φ(x+) arising from the NS-NS sector alone, the source w... |

6 |
Light-like Big Bang singularities in string and matrix
- Craps, Evnin
(Show Context)
Citation Context ...nerality, allowing for possible inhomogeneities, i.e. with g++ having spatial (xi) dependence. These are near horizon limits of D3-brane analogs of plane-waves with possible inhomogeneities (see e.g. =-=[28]-=- for a recent review discussing plane-wave backgrounds [29] in the context of cosmological singularities). Since AdS5 × S5 is α′-exact [30] as are plane wave spacetimes, these AdS null deformations ar... |

2 |
Electric/magnetic deformations of S**3 and AdS(3), and geometric cosets,” Fortsch. Phys
- Israel, Kounnas, et al.
(Show Context)
Citation Context ...a proof that all higher derivative corrections to (2) vanish, it is suggestive, making these AdS plane waves potentially more interesting (some earlier work on similar α′-exact backgrounds appears in =-=[31]-=-). We will mainly focus here on null deformations with g++(xi, r), which can all be thought of as simply solutions to 5-dim gravity with negative cosmological constant, satisfying RMN = −4gMN (M,N = µ... |

1 |
Cosmological singularities, AdS/CFT and de Sitter deformations,” arXiv:1204.3506 [hepth
- Narayan
- 2011
(Show Context)
Citation Context ...ning on the sources g(0), Φ(0). 3See e.g. [41, 42, 43, 44] for recent discussions of holographic renormalization in Lifshitz backgrounds; see also [38]. 13 These arguments have also been discussed in =-=[46]-=- in the cosmological singularities context of [45, 40]. This discussion on the Fefferman-Graham expansion is mainly based on the foliation where we have g(0) 6= 0 alone: however the relation between g... |

1 | Skenderis ”Asymptotically Anti-de Sitter spacetimes and their stress energy tensor - unknown authors |