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## Boundary Stress-Energy Tensor and Newton-Cartan Geometry

Venue: | in Lifshitz Holography, JHEP 1401 (2014) 057. arXiv:1311.6471, doi:10.1007/JHEP01(2014)057 |

Citations: | 1 - 0 self |

### Citations

5604 | The large N limit of superconformal field theories and supergravity
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- 1998
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Citation Context ... Density 56 D Holographic Reconstruction 58 E A Hyperscaling θ = −1 and z = 1 UV Completion 60 References 61 1 Introduction 1.1 Scope and Motivation Ever since the birth of the AdS/CFT correspondence =-=[1]-=- there has been a continuous effort to find more examples of holographic correspondences. In recent years this has received an extra boost due to the growing interest in using holography as a tool to ... |

453 |
Holographic reconstruction of spacetime and renormalization
- Haro, Solodukhin, et al.
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Citation Context ...l give the solutions of the equations of motion up to NNLO and discuss the local and anomaly counterterms as well as the one-point functions for asymptotically locally AdS (AlAdS) boundary conditions =-=[61, 62]-=-. A.1 Fefferman–Graham expansions and counterterms The solution to equations (2.2)–(2.4) expressed as an asymptotic series in radial gauge, i.e. as a Fefferman–Graham (FG) expansion [63], reads18 ĝµ̂... |

247 |
Conformal invariants, Élie Cartan et les Mathmatiques d’Aujourd’hui, Asterisque
- Fefferman, Graham
- 1985
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Citation Context ...onditions [61, 62]. A.1 Fefferman–Graham expansions and counterterms The solution to equations (2.2)–(2.4) expressed as an asymptotic series in radial gauge, i.e. as a Fefferman–Graham (FG) expansion =-=[63]-=-, reads18 ĝµ̂ν̂dx µ̂dxν̂ = dr2 r2 + ĥâb̂dx âdxb̂ , (A.1) ĥâb̂ = 1 r2 [ ĥ(0)âb̂ + r 2ĥ(2)âb̂ + r 4 log rĥ(4,1)âb̂ + r 4ĥ(4)âb̂ +O(r 6 log r) ] , (A.2) φ̂ = φ̂(0) + r 2φ̂(2) + r 4 log rφ̂(... |

160 |
The holographic Weyl anomaly, JHEP 9807
- Henningson, Skenderis
- 1998
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Citation Context ...o do the same for the current term because we expect that the term ∂a ( e(0)J a (0) ) can be removed by adding finite counterterms to the action just like in the context of the AdS/CFT correspondence =-=[54]-=-. As remarked at the beginning of this section the only assumption that we made was that τ(0)a is hypersurface orthogonal. This means that in the language of section 2.3 this result applies to the cas... |

150 | Holographic duality with a view toward many-body physics,” arXiv:0909.0518 - McGreevy |

145 |
Effective holographic theories for low-temperature condensed matter systems,”
- Charmousis, Gouteraux, et al.
- 2010
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Citation Context ...hitz symmetry group (z-dependent scale transformations t → λzt, ~x → λ~x, space-time translations and spatial rotations). Lifshitz geometries [3, 4, 5] together with hyperscaling violating geometries =-=[6, 7, 8]-=- as well as more general Bianchi type space-times [9] have occurred as effective IR geometries that could furnish as a groundstate geometry of some CM system. Depending on one’s interest one can then ... |

134 |
Gravity duals for non-relativistic CFTs,” Phys
- Balasubramanian, McGreevy
- 2008
(Show Context)
Citation Context ...es of the analogue Fefferman–Graham (FG) theorem which so far is only known when contact with an AdS space-time can be made (e.g. by dualities such as TsT in the case of z = 2 Schrödinger holography =-=[10, 11, 12, 13]-=- or by dimensional reduction as in the case of z = 2 Lifshitz holography which will be elaborated on further below). As a result, many properties of the holographic dictionary such as the boundary geo... |

106 | Membranes at Quantum Criticality
- Hořava
(Show Context)
Citation Context ...ative terms built out of curvatures and projected covariant derivatives. These are thus gradient potential terms. This Lagrangian has striking similarities with Hořava–Lifshitz (HL) type Lagrangians =-=[55]-=-. For example pushing this analogy we would call TTNC with furthermore ∂aτ(0)b−∂bτ(0)a = 0 projectable Hořava–Lifshitz and TTNC with nonzero ∂aτ(0)b − ∂bτ(0)a non-projectable HL gravity. Furthermore,... |

104 |
Non-relativistic holography,” [arXiv:0812.0530 [hep-th
- Taylor
(Show Context)
Citation Context ...me quantum critical point that is invariant under the Lifshitz symmetry group (z-dependent scale transformations t → λzt, ~x → λ~x, space-time translations and spatial rotations). Lifshitz geometries =-=[3, 4, 5]-=- together with hyperscaling violating geometries [6, 7, 8] as well as more general Bianchi type space-times [9] have occurred as effective IR geometries that could furnish as a groundstate geometry of... |

104 |
Sur les variétés à connexion affine et la théorie de la relativité généralisée (deuxiéme partie
- Cartan
- 1925
(Show Context)
Citation Context ...metry will also play an important role in our expression for the anomaly. In particular, we will show that in the case of a τ(0)a satisfying ∂aτ(0)b−∂bτ(0)a = 0 the boundary geometry is Newton–Cartan =-=[44, 45]-=- (see also [46]) and that a nonzero ∂aτ(0)b − ∂bτ(0)a corresponds to adding torsion. The appearance of Newton-Cartan structures is expected as the boundary geometry is obtained by null-dimensional red... |

100 |
Hidden Fermi surfaces in compressible states of gauge-gravity duality,”
- Huijse, Sachdev, et al.
- 2012
(Show Context)
Citation Context ...hitz symmetry group (z-dependent scale transformations t → λzt, ~x → λ~x, space-time translations and spatial rotations). Lifshitz geometries [3, 4, 5] together with hyperscaling violating geometries =-=[6, 7, 8]-=- as well as more general Bianchi type space-times [9] have occurred as effective IR geometries that could furnish as a groundstate geometry of some CM system. Depending on one’s interest one can then ... |

81 |
Thermodynamics of asymptotically locally AdS spacetimes
- Papadimitriou, Skenderis
- 2005
(Show Context)
Citation Context ...l give the solutions of the equations of motion up to NNLO and discuss the local and anomaly counterterms as well as the one-point functions for asymptotically locally AdS (AlAdS) boundary conditions =-=[61, 62]-=-. A.1 Fefferman–Graham expansions and counterterms The solution to equations (2.2)–(2.4) expressed as an asymptotic series in radial gauge, i.e. as a Fefferman–Graham (FG) expansion [63], reads18 ĝµ̂... |

74 |
Aspects of holography for theories with hyperscaling violation,
- Dong, Harrison, et al.
- 2012
(Show Context)
Citation Context ...hitz symmetry group (z-dependent scale transformations t → λzt, ~x → λ~x, space-time translations and spatial rotations). Lifshitz geometries [3, 4, 5] together with hyperscaling violating geometries =-=[6, 7, 8]-=- as well as more general Bianchi type space-times [9] have occurred as effective IR geometries that could furnish as a groundstate geometry of some CM system. Depending on one’s interest one can then ... |

70 |
Lifshitz spacetimes from AdS null and cosmological solutions,
- Balasubramanian, Narayan
- 2010
(Show Context)
Citation Context ...ns of motion. Such a scenario is known to be possible when z = 2 for the following reason. A Lifshitz space-time with z = 2 can be uplifted to an asymptotically AdS space-time in one dimension higher =-=[33, 34]-=-. This observation has motivated the search for Lagrangians that in 4 dimensions admit z = 2 Lifshitz solutions and that can be uplifted to 5 dimensions where they admit asymptotically AdS solutions [... |

62 |
Holographic stress tensor for non-relativistic theories,” arXiv:0907.1846 [hep-th
- Ross, Saremi
(Show Context)
Citation Context ..., 5] because it is simple in matter content and because it can account for all values of z by suitably choosing the cosmological constant and mass parameter. For a holographic study of this model see =-=[14, 15, 16, 17, 18, 19]-=-. From an analysis of the linearized perturbations [20, 14, 15, 16] it is known that one must separately study the following three cases: i). 1 < z < 2, ii). z = 2 (see also [21, 22, 23]) and iii). z ... |

58 | Black Holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent,” arXiv:0905.3183 [hep-th
- Bertoldi, Burrington, et al.
(Show Context)
Citation Context ...z = 2 (see also [21, 22, 23]) and iii). z > 2. For a perturbative approach to values of z close to one see the recent works [24]. Black hole solutions of the massive vector model have been studied in =-=[20, 25, 26]-=-. For related work on solutions such as Lifshitz black holes in other models for Lifshitz holography see e.g. [5, 27, 28, 29]. Probe fields and correlation functions have been studied in [4, 5, 30, 31... |

57 | Precision holography for non-conformal branes
- Kanitscheider, Skenderis, et al.
(Show Context)
Citation Context ...hitz which is such that the next item is weaker than the previous one. For each of these boundary conditions we list the corresponding 4 boundary geometry in table 1. The reduction suggests (see also =-=[42]-=-) that the 4-dimensional asymptotic expansions are naturally formulated in a non-radial gauge. The section concludes with a discussion of the issues one faces when trying to transform to radial gauge.... |

56 |
From gauge-string duality to strong interactions: a Pedestrian’s Guide
- Gubser, Karch
- 2009
(Show Context)
Citation Context ...r purposes (see the discussion in section 2.4) it will prove convenient to work up to second order by which we mean that we expand the pure gauge perturbation δgµν as follows δgµν = δ[1]gµν + 1 2 2δ=-=[2]-=-gµν +O( 3) . (B.3) To achieve this we transform the left hand side using (see e.g. [65]) r = r′ − ξr(r′, x′) + 1 2 ξν∂′νξ r +O(3) , xa = x′a − ξa(r′, x′) + 1 2 ξν∂′νξ a +O(3) , (B.4) where we expan... |

56 | Black holes in asymptotically Lifshitz spacetime
- Danielsson, Thorlacius
(Show Context)
Citation Context ...all values of z by suitably choosing the cosmological constant and mass parameter. For a holographic study of this model see [14, 15, 16, 17, 18, 19]. From an analysis of the linearized perturbations =-=[20, 14, 15, 16]-=- it is known that one must separately study the following three cases: i). 1 < z < 2, ii). z = 2 (see also [21, 22, 23]) and iii). z > 2. For a perturbative approach to values of z close to one see th... |

52 |
Constructing Lifshitz solutions from AdS,
- Cassani, Faedo
- 2011
(Show Context)
Citation Context ...]. This observation has motivated the search for Lagrangians that in 4 dimensions admit z = 2 Lifshitz solutions and that can be uplifted to 5 dimensions where they admit asymptotically AdS solutions =-=[35, 36, 37]-=-. The central idea is then to construct the FG expansions of the solutions in 5 dimensions and to reduce this to 4 dimensions. A first step in this direction was taken in [38] where the focus was on d... |

50 | Quantum Gravity at a Lifshitz Point - Hořava |

49 |
A field-theory motivated approach to symbolic computer algebra
- Peeters
(Show Context)
Citation Context ...missany, Kristian Holsheimer, Elias Kiritsis, Ioannis Papadimitriou, Simon Ross, Marika Taylor and Lárus Thorlacius for useful discussions. Some of the calculations have been performed using Cadabra =-=[60]-=-. The work of JH and NO is supported in part by the Danish National Research Foundation project “Black holes and their role in quantum gravity”. BR acknowledges support from the Swiss National Science... |

44 |
On Existence of Self-Tuning Solutions
- Koroteev, Libanov
- 2008
(Show Context)
Citation Context ...me quantum critical point that is invariant under the Lifshitz symmetry group (z-dependent scale transformations t → λzt, ~x → λ~x, space-time translations and spatial rotations). Lifshitz geometries =-=[3, 4, 5]-=- together with hyperscaling violating geometries [6, 7, 8] as well as more general Bianchi type space-times [9] have occurred as effective IR geometries that could furnish as a groundstate geometry of... |

44 | Perturbations of spacetime: Gauge transformations and gauge invariance at second order and beyond
- Bruni, Matarrese, et al.
- 1997
(Show Context)
Citation Context ...econd order by which we mean that we expand the pure gauge perturbation δgµν as follows δgµν = δ[1]gµν + 1 2 2δ[2]gµν +O( 3) . (B.3) To achieve this we transform the left hand side using (see e.g. =-=[65]-=-) r = r′ − ξr(r′, x′) + 1 2 ξν∂′νξ r +O(3) , xa = x′a − ξa(r′, x′) + 1 2 ξν∂′νξ a +O(3) , (B.4) where we expand ξµ as ξµ = ξµ[1] + 1 2 2ξµ[2] +O( 3) . (B.5) The metric in the primed coordinate sy... |

42 | Holography for asymptotically locally Lifshitz spacetimes - Ross |

41 |
Counter-term charges generate bulk symmetries,” arXiv:hep-th/0503105
- Hollands, Ishibashi, et al.
(Show Context)
Citation Context ...ry stress-energy tensor is not of the form of a conservation equation. This is common for stress-energy tensors defined by variation with respect to vielbeins whenever there are vectors in the theory =-=[43]-=-. The main difference between T a(0)b and the HIM [43] boundary stress-energy tensor is due to the TNC boundary geometry, i.e. the fact that we cannot raise/lower indices and the presence of torsion. ... |

41 |
Spinor and twistor methods in space-time geometry
- Vol
- 1986
(Show Context)
Citation Context ...alings of the boundary metric preserve this foliation. Conformal rescalings of the boundary metric ĥ(0)âb̂ and boundary diffeomorphisms are generated by Penrose–Brown–Henneaux (PBH) transformations =-=[64]-=-, i.e. diffeomorphisms that preserve the gauge choice of the FG expansion. Infinitesimally these transformations act on the 5-dimensional fields as δĝµ̂ν̂ = Lξ̂ ĝµ̂ν̂ , (A.41) δφ̂ = Lξ̂φ̂ , (A.42) δ... |

25 |
Holographic models for theories with hyperscaling violation,
- Gath, Hartong, et al.
- 2013
(Show Context)
Citation Context ...s than our model). In that model for z = 2 we have 5+5 free functions in the expansion. The way we came to this answer is as follows. Using the equations for the linearized perturbation analysis17 of =-=[58]-=- (setting the parameters a and b defined in [58] equal to zero and truncating the scalar field) we observe by looking at purely radial perturbations around Lifshitz that there are 4 integration consta... |

23 |
Holographic renormalization of general dilaton-axion gravity,
- Papadimitriou
- 2011
(Show Context)
Citation Context ...o the boundary space-time and underlined indices denote tangent space. Our input will be the FG expansion of the solution to the equations of motion of the 5-dimensional action near the boundary (see =-=[40, 38]-=-), along with the identification of the sources and vevs in this model and the Ward identities satisfied by the vevs. The reduction from 5 to 4 dimensions is a ScherkSchwarz reduction which we choose ... |

22 |
From D3-branes to Lifshitz space-times,
- Chemissany, Hartong
- 2011
(Show Context)
Citation Context ...]. This observation has motivated the search for Lagrangians that in 4 dimensions admit z = 2 Lifshitz solutions and that can be uplifted to 5 dimensions where they admit asymptotically AdS solutions =-=[35, 36, 37]-=-. The central idea is then to construct the FG expansions of the solutions in 5 dimensions and to reduce this to 4 dimensions. A first step in this direction was taken in [38] where the focus was on d... |

21 | Holography for chiral scale-invariant models,
- Costa, Taylor
- 2011
(Show Context)
Citation Context ...ns of motion. Such a scenario is known to be possible when z = 2 for the following reason. A Lifshitz space-time with z = 2 can be uplifted to an asymptotically AdS space-time in one dimension higher =-=[33, 34]-=-. This observation has motivated the search for Lagrangians that in 4 dimensions admit z = 2 Lifshitz solutions and that can be uplifted to 5 dimensions where they admit asymptotically AdS solutions [... |

20 |
Holographic renormalization for asymptotically Lifshitz spacetimes,
- Mann, McNees
- 2011
(Show Context)
Citation Context ..., 5] because it is simple in matter content and because it can account for all values of z by suitably choosing the cosmological constant and mass parameter. For a holographic study of this model see =-=[14, 15, 16, 17, 18, 19]-=-. From an analysis of the linearized perturbations [20, 14, 15, 16] it is known that one must separately study the following three cases: i). 1 < z < 2, ii). z = 2 (see also [21, 22, 23]) and iii). z ... |

17 |
Anomalous Breaking of Anisotropic Scaling
- Baggio, Boer, et al.
(Show Context)
Citation Context ..., 5] because it is simple in matter content and because it can account for all values of z by suitably choosing the cosmological constant and mass parameter. For a holographic study of this model see =-=[14, 15, 16, 17, 18, 19]-=-. From an analysis of the linearized perturbations [20, 14, 15, 16] it is known that one must separately study the following three cases: i). 1 < z < 2, ii). z = 2 (see also [21, 22, 23]) and iii). z ... |

17 |
Black holes and black branes
- Tarrio, Vandoren
(Show Context)
Citation Context ...s [24]. Black hole solutions of the massive vector model have been studied in [20, 25, 26]. For related work on solutions such as Lifshitz black holes in other models for Lifshitz holography see e.g. =-=[5, 27, 28, 29]-=-. Probe fields and correlation functions have been studied in [4, 5, 30, 31, 32]. As an alternative approach one could give up generality and study a specific model where z is fixed but with the advan... |

16 |
Lifshitz solutions in supergravity and string theory,
- Gregory, Parameswaran, et al.
- 2010
(Show Context)
Citation Context ...s [24]. Black hole solutions of the massive vector model have been studied in [20, 25, 26]. For related work on solutions such as Lifshitz black holes in other models for Lifshitz holography see e.g. =-=[5, 27, 28, 29]-=-. Probe fields and correlation functions have been studied in [4, 5, 30, 31, 32]. As an alternative approach one could give up generality and study a specific model where z is fixed but with the advan... |

16 |
Null Killing vector dimensional reduction and Galilean geometrodynamics,” Nucl.Phys. B439
- Julia, Nicolai
- 1995
(Show Context)
Citation Context ...udying geometries obtained by dimensional reduction along a null circle generated by a hypersurface orthogonal null Killing vector which is not necessarily parallel. Such cases have been looked at in =-=[48]-=- and from the work of [49] it is expected that the connection on the reduced 3-dimensional boundary will have torsion. We will also study the more general case where ∂u is a null Killing vector but no... |

15 | Holographic Renormalization for z=2 Lifshitz Space-Times from AdS”,
- Chemissany, Geissbuhler, et al.
- 2012
(Show Context)
Citation Context ...ly AdS solutions [35, 36, 37]. The central idea is then to construct the FG expansions of the solutions in 5 dimensions and to reduce this to 4 dimensions. A first step in this direction was taken in =-=[38]-=- where the focus was on deriving the counterterms in 4 dimensions. Using this philosophy, we have presented in [39] the basic ingredients of an explicit holographic dictionary for Lifshitz holography ... |

14 |
Uber den Newtonschen Grenzwert der Einsteinschen Gravitationstheorie. In
- Ehlers
- 1981
(Show Context)
Citation Context ...metry will also play an important role in our expression for the anomaly. In particular, we will show that in the case of a τ(0)a satisfying ∂aτ(0)b−∂bτ(0)a = 0 the boundary geometry is Newton–Cartan =-=[44, 45]-=- (see also [46]) and that a nonzero ∂aτ(0)b − ∂bτ(0)a corresponds to adding torsion. The appearance of Newton-Cartan structures is expected as the boundary geometry is obtained by null-dimensional red... |

7 | Holographic flows to IR Lifshitz spacetimes
- Singh
(Show Context)
Citation Context ...s depend on whether the reduction is along a circle that becomes asymptotically null or one that is asymptotically spacelike leading to two different UV completions from a 4-dimensional point of view =-=[57]-=-. It would in fact be interesting to work out the details of the computation of the sources and vevs in that case. The fact that for our Lifshitz UV completion we count in total 6+6+1 free functions i... |

6 |
Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics
- Hartong, Rollier
(Show Context)
Citation Context ...es of the analogue Fefferman–Graham (FG) theorem which so far is only known when contact with an AdS space-time can be made (e.g. by dualities such as TsT in the case of z = 2 Schrödinger holography =-=[10, 11, 12, 13]-=- or by dimensional reduction as in the case of z = 2 Lifshitz holography which will be elaborated on further below). As a result, many properties of the holographic dictionary such as the boundary geo... |

6 |
An Isotropic to Anisotropic Transition in a Fractional Quantum
- Mulligan, Nayak, et al.
(Show Context)
Citation Context ...ns. Further since the reduction is along a null circle (from a boundary perspective) the theory will have a z = 2 dynamical exponent. It has therefore been dubbed a Lifshitz–Chern–Simons gauge theory =-=[41]-=-. Hence a specific subset of the 5-dimensional asymptotically AdS solutions can be reduced to 4-dimensional asymptotically Lifshitz geometries [38] while maintaining a well-defined low energy approxim... |

6 |
On the Newtonian Limit of General Relativity
- Dautcourt
- 1990
(Show Context)
Citation Context ...= 0 , (4.65) D(0)aei(0)b = 0 , (4.66) D(0)aeb(0)i = 0 . (4.67) This implies ∇(0)aΠbc(0) = 0 , (4.68) ∇(0)aτ(0)b = 0 . (4.69) Provided we have ∂aτ(0)b − ∂bτ(0)a = 0 the Γa(0)bc is of the form given in =-=[51, 50]-=- and of the form used in [52] if furthermore F(0)ab = 0. 25 We remark that one should not confuse Newton–Cartan geometry with Newtonian gravity11. This requires additional conditions such as the so-ca... |

5 |
Flows involving Lifshitz solutions, Class.Quant.Grav
- Braviner, Gregory, et al.
(Show Context)
Citation Context ...s [24]. Black hole solutions of the massive vector model have been studied in [20, 25, 26]. For related work on solutions such as Lifshitz black holes in other models for Lifshitz holography see e.g. =-=[5, 27, 28, 29]-=-. Probe fields and correlation functions have been studied in [4, 5, 30, 31, 32]. As an alternative approach one could give up generality and study a specific model where z is fixed but with the advan... |

4 |
Particle Number and 3D Schroedinger Holography,” arXiv:1305.3653 [hep-th
- Hartong, Rollier
(Show Context)
Citation Context ...es of the analogue Fefferman–Graham (FG) theorem which so far is only known when contact with an AdS space-time can be made (e.g. by dualities such as TsT in the case of z = 2 Schrödinger holography =-=[10, 11, 12, 13]-=- or by dimensional reduction as in the case of z = 2 Lifshitz holography which will be elaborated on further below). As a result, many properties of the holographic dictionary such as the boundary geo... |

4 |
What do non-relativistic CFTs tell us about Lifshitz spacetimes?,” arXiv:1308.5689 [hep-th
- Keeler, Knodel, et al.
(Show Context)
Citation Context ... [20, 25, 26]. For related work on solutions such as Lifshitz black holes in other models for Lifshitz holography see e.g. [5, 27, 28, 29]. Probe fields and correlation functions have been studied in =-=[4, 5, 30, 31, 32]-=-. As an alternative approach one could give up generality and study a specific model where z is fixed but with the advantage that one controls the asymptotic expansions to the equations of motion. Suc... |

3 |
et al., “Bianchi Attractors: A
- Iizuka, Kachru, et al.
(Show Context)
Citation Context ...λzt, ~x → λ~x, space-time translations and spatial rotations). Lifshitz geometries [3, 4, 5] together with hyperscaling violating geometries [6, 7, 8] as well as more general Bianchi type space-times =-=[9]-=- have occurred as effective IR geometries that could furnish as a groundstate geometry of some CM system. Depending on one’s interest one can then consider either an AdS (with or without hyperscaling ... |

3 | Deformations of CFTs and Holography”, - Baggio - 2013 |

3 |
Lifshitz as a deformation of Anti-de Sitter,” arXiv:1304.7776
- Korovin, Skenderis, et al.
(Show Context)
Citation Context ...at one must separately study the following three cases: i). 1 < z < 2, ii). z = 2 (see also [21, 22, 23]) and iii). z > 2. For a perturbative approach to values of z close to one see the recent works =-=[24]-=-. Black hole solutions of the massive vector model have been studied in [20, 25, 26]. For related work on solutions such as Lifshitz black holes in other models for Lifshitz holography see e.g. [5, 27... |

3 |
Galilei and lorentz structures on space-time - comparison of the corresponding geometry and physics,” Annales Poincare Phys.Theor
- Kuenzle
- 1972
(Show Context)
Citation Context ... by dimensional reduction along a null circle generated by a hypersurface orthogonal null Killing vector which is not necessarily parallel. Such cases have been looked at in [48] and from the work of =-=[49]-=- it is expected that the connection on the reduced 3-dimensional boundary will have torsion. We will also study the more general case where ∂u is a null Killing vector but not necessarily hypersurface... |

3 | A non–relativistic Weyl anomaly
- Adam, Melnikov, et al.
(Show Context)
Citation Context ...urvature term. In the notation of [19] these are denoted by C1 and C2, respectively (see [38] for their appropriately normalized values). For other examples of Lifshitz anisotropic Weyl anomalies see =-=[56, 19]-=-. When I(0) 6= 0 there is one more term in the anomaly density. This is the term at order k4. It would be interesting to understand better the role of this non-derivative term. 43 6.3 Irrelevant defor... |

2 |
A Fefferman-Graham-Like Expansion for
- Guica
(Show Context)
Citation Context |

2 | Logarithmic two-Point Correlation Functions from a z = 2 Lifshitz Model,” arXiv:1310.4778 [hep-th
- Zingg
(Show Context)
Citation Context ... [20, 25, 26]. For related work on solutions such as Lifshitz black holes in other models for Lifshitz holography see e.g. [5, 27, 28, 29]. Probe fields and correlation functions have been studied in =-=[4, 5, 30, 31, 32]-=-. As an alternative approach one could give up generality and study a specific model where z is fixed but with the advantage that one controls the asymptotic expansions to the equations of motion. Suc... |

1 | Stringy Schrdinger truncations,” JHEP 1308 - Detournay, Guica - 2013 |

1 | On the Marginally Relevant Operator
- Holsheimer
(Show Context)
Citation Context ...e [14, 15, 16, 17, 18, 19]. From an analysis of the linearized perturbations [20, 14, 15, 16] it is known that one must separately study the following three cases: i). 1 < z < 2, ii). z = 2 (see also =-=[21, 22, 23]-=-) and iii). z > 2. For a perturbative approach to values of z close to one see the recent works [24]. Black hole solutions of the massive vector model have been studied in [20, 25, 26]. For related wo... |

1 | Boundary conditions for scalars in Lifshitz,” Class.Quant.Grav. 30 (2013) 065009, arXiv:1212.2572 [hep-th - Andrade, Ross |

1 |
Dynamical Trajectories and Geodesics,” Annals of Mathematics 30
- Eisenhart
- 1928
(Show Context)
Citation Context ...ary geometry. The relation between null dimensional reduction along a circle parametrized by u of a space-time with a parallel (covariantly constant) ∂u and Newton–Cartan geometry has been studied in =-=[47]-=-. The covector ĥ(0)âb̂(∂u) b̂ is equal to δaâτ(0)a as given by (3.53). Since the 5-dimensional boundary metric ĥ(0)âb̂ is only defined up to conformal rescalings we naturally need to be able to d... |

1 |
Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity,” arXiv:1309.6794 [hep-th
- arXiv
(Show Context)
Citation Context ...esting to use our results in the context of Lifshitz black holes and Lifshitz hydrodynamics. In particular, it would be interesting to obtain a fluid/gravity type derivation of Lifshitz hydrodynamics =-=[59]-=- which has potential applications to holographic realizations of Son’s model for the effective theory of the fractional quantum Hall effect that relies on Newton–Cartan geometry [52]. Acknowledgements... |