### Citations

1142 | Quantization of Gauge Systems - Henneaux, Teitelboim - 1992 |

453 | Holographic reconstruction of spacetime and renormalization - Haro, Solodukhin, et al. |

388 | Supergravity and the large N limit of theories with sixteen supercharges,” Phys. Rev. D58
- Itzhaki, Maldacena, et al.
- 1998
(Show Context)
Citation Context ... it belongs to case II. It is well known that there are no well defined Fefferman-Graham asymptotic expansions in the case of D6 branes [18], which reflects the fact that there is no decoupling limit =-=[15]-=-. A general criterion for the existence of well defined asymptotic expansions is the volume divergence of the on-shell action. For the metric (1.1) in the Einstein frame we get S ∼ ˆ du ud+z+1−θ , (1.... |

300 |
Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry,” Phys
- Son
(Show Context)
Citation Context ... the strongly coupled dynamics of condensed matter systems has attracted considerable interest in the last few years. Gravity duals to quantum critical points exhibiting Lifshitz [3–5] or Schrödinger =-=[6, 7]-=- symmetry have been put forward and studied extensively. More recently, scaling geometries where translations in the radial coordinate is not an isometry but only a conformal isometry have been propos... |

236 |
Handbook of exact solutions for ordinary differential equations, Boca Raton,
- Polyanin, Zaitsev
- 1995
(Show Context)
Citation Context ...ition (3.43) determines that w(y) must satisfy w(yo) = d(1 + µξ) + z − 1, w′(yo) = −, yo := Yo(X)Zξ(X) = −z − 1 2 . (3.50) Equation (3.48) can be transformed into an Abel equation of the first kind =-=[54]-=-, which is in general non-integrable. For special ranges of the parameters it admits analytic solutions of the form w = √ a+ by, which are special cases of the more general class of solutions derived ... |

159 | The Holographic Weyl anomaly, JHEP 9807 - Henningson, Skenderis - 1998 |

145 |
Effective holographic theories for low-temperature condensed matter systems,”
- Charmousis, Gouteraux, et al.
- 2010
(Show Context)
Citation Context ... dν1(νz − ν1 + 1) = 0, (3.31) Q2 = Zo 2 (νz − ν1)(νz + dν1 − 1 + dξµ), Vo = − (νz + (d− 1)ν1 + dξµ) (νz + dν1 − 1 + dξµ) . – 14 – These solutions are related to the finite charge density solutions in =-=[53]-=-. Note that, as for the Lifshitz solutions, there is a limiting case of this class of solutions that has Q = 0 and νz +dν1−1 +dξµ = 0. For ξ = 0 this is the corresponding Lifshitz solution we discusse... |

134 |
Gravity duals for non-relativistic CFTs,” Phys
- Balasubramanian, McGreevy
- 2008
(Show Context)
Citation Context ... the strongly coupled dynamics of condensed matter systems has attracted considerable interest in the last few years. Gravity duals to quantum critical points exhibiting Lifshitz [3–5] or Schrödinger =-=[6, 7]-=- symmetry have been put forward and studied extensively. More recently, scaling geometries where translations in the radial coordinate is not an isometry but only a conformal isometry have been propos... |

115 | Exploring improved holographic theories for QCD: Part I”,
- Gürsoy, Kiritsis
- 2008
(Show Context)
Citation Context ... 3For ∆+ = (d+ z + dµξ)/2 the Breitenlohner-Freedman (BF) bound [55, 56] is saturated and various logarithmic terms appear starting at order (y − yo)2 log |y − yo|. – 18 – of Improved Holographic QCD =-=[37, 57, 58]-=- and it is important in order to correctly renormalize the often studied Einstein-Proca theory for d = z = 2 when the marginally relevant deformation y − yo is turned on as in e.g. [59]. All terms mus... |

100 | Hidden Fermi surfaces in compressible states of gauge-gravity duality,” - Huijse, Sachdev, et al. - 2012 |

90 |
D.: Stability in gauged extended supergravity
- Breitenlohner, Freedman
- 1982
(Show Context)
Citation Context ... must be kept in this case to obtain the correct asymptotic solution of the HJ equation. This is reminiscent of what happens in the case 3For ∆+ = (d+ z + dµξ)/2 the Breitenlohner-Freedman (BF) bound =-=[55, 56]-=- is saturated and various logarithmic terms appear starting at order (y − yo)2 log |y − yo|. – 18 – of Improved Holographic QCD [37, 57, 58] and it is important in order to correctly renormalize the o... |

74 | Non-relativistic holography
- Taylor
(Show Context)
Citation Context ..., θ ≤ d, or θ ≥ d(z − 1), for z > 2, (3.21) which are compatible with the NEC solutions III-V provided also θ < d+ z. Setting ξ = 0 in these solutions we recover the anisotropic solutions obtained in =-=[5]-=-. Note that necessarily µ 6= 0 in this case, and so a running scalar is required to support these solutions. The limiting case θ = d+z leads to Q = 0 and was discussed in [24]. However there are more ... |

74 |
Aspects of holography for theories with hyperscaling violation,
- Dong, Harrison, et al.
- 2012
(Show Context)
Citation Context ...unds. As for Dp branes, the holographic relation between the energy scale of the dual field theory and the radial coordinate u can be unambiguously identified through a supergravity probe calculation =-=[20, 21]-=-. This determines that the ultraviolet (UV) of the dual theory is located at u = 0, independently of the value of θ, in agreement with the relativistic case z = 1 [15–19]. It follows that the proper i... |

70 |
Fake supergravity and domain wall stability, Phys. Rev. D69
- Freedman, Nunez, et al.
- 2004
(Show Context)
Citation Context ...an ansatz for a class of background solutions, these first order equations become analogous to first order BPS equations, while Hamilton’s principal function S plays the role of a fake superpotential =-=[51]-=-. We will discuss this in detail in Section 3. The second major application of these equations will be to obtain the asymptotic Fefferman-Graham expansions of the fields, and as a result the holograph... |

63 |
Correlation functions
- Papadimitriou, Skenderis
(Show Context)
Citation Context ... In the Poincaré domain wall example this is the well known fact that only a superpotential with a quadratic term that corresponds to a deformation can be used to construct the holographic dictionary =-=[52]-=-. Constructing such an asymptotic complete integral and deriving the holographic map for asymptotically Lifshitz and hvLf backgrounds is the main purpose of this paper. We now describe this constructi... |

62 | Macroscopic superstrings as interpolating solitons,” Phys. Lett. B332
- Duff, Gibbons, et al.
- 1994
(Show Context)
Citation Context ...elativistic case z = 1 [15–19]. It follows that the proper identification of the boundary of the geometry (1.1) through a conformal compactification requires a Weyl transformation to the “dual frame” =-=[18, 22]-=-, where the metric becomes Lifshitz, thus providing an unambiguous definition of the boundary. In the conformal case, θ = 0, such a potential ambiguity does not arise since no field redefinition (incl... |

62 |
Holographic stress tensor for non-relativistic theories,” arXiv:0907.1846 [hep-th
- Ross, Saremi
(Show Context)
Citation Context ...ned in order to obtain an exact background solution. Backgrounds with w̃n = 0 can be obtained through the recursion relations (3.58) applied to any n > 2. These results are in agreement with those of =-=[1, 27, 31]-=-, which were obtained through an analysis of the linearized fluctuations of the equations of motion. Here we have derived these in a simpler way using only the superpotential equation (3.10). There is... |

57 | Precision holography for non-conformal branes
- Kanitscheider, Skenderis, et al.
(Show Context)
Citation Context ...elativistic case z = 1 [15–19]. It follows that the proper identification of the boundary of the geometry (1.1) through a conformal compactification requires a Weyl transformation to the “dual frame” =-=[18, 22]-=-, where the metric becomes Lifshitz, thus providing an unambiguous definition of the boundary. In the conformal case, θ = 0, such a potential ambiguity does not arise since no field redefinition (incl... |

53 | Holographic renormalization and Ward identities with the Hamilton-Jacobi method, - Martelli, Mueck - 2003 |

44 | On Existence of Self-Tuning Solutions - Koroteev, Libanov - 2008 |

42 |
Holography for asymptotically locally Lifshitz spacetimes
- Ross
(Show Context)
Citation Context ...ased on the covariant expansion of the HJ solution in eigenfunctions of a suitable operator. For scale invariant boundary conditions this operator is usually the relativistic [44] or non-relativistic =-=[29, 33]-=- dilatation operator. For more general boundary conditions, such as non-conformal branes or hvLf backgrounds, a generalized dilatation operator is required, such as the one discussed in [37] for relat... |

30 | On the holographic renormalization group,” JHEP 0008 - Boer, Verlinde, et al. - 2000 |

25 |
Holographic models for theories with hyperscaling violation,
- Gath, Hartong, et al.
- 2013
(Show Context)
Citation Context ...pic solutions obtained in [5]. Note that necessarily µ 6= 0 in this case, and so a running scalar is required to support these solutions. The limiting case θ = d+z leads to Q = 0 and was discussed in =-=[24]-=-. However there are more solutions with Q = 0 which we discuss now. ii) Wo = 0, Q = 0: This case also corresponds to a massless U(1) gauge field but now the gauge field in not switched on in the backg... |

23 |
Holographic renormalization of general dilaton-axion gravity,
- Papadimitriou
- 2011
(Show Context)
Citation Context ...n was utilized in [36] in order to deduce the holographic dictionary for the Lifshitz backgrounds from the dictionary for asymptotically locally AdS solutions of the axion-dilaton theory developed in =-=[37]-=-. The same model was revisited in [38, 39] using the vielbein formalism and a connection between the structure of the sources and Newton-Cartan geometry on the boundary was proposed. Another way to re... |

22 |
From D3-branes to Lifshitz space-times,
- Chemissany, Hartong
- 2011
(Show Context)
Citation Context ... backgrounds of the Einstein-Proca theory, there are few examples where the non-relativistic dictionary has been inferred from a related relativistic dictionary for asymptotically AdS backgrounds. In =-=[35]-=- a 4-dimensional model that admits z = 2 Lifshitz backgrounds was obtained by a dimensional reduction of an axion-dilaton system in 5 dimensions that can be embedded in Type IIB supergravity. In parti... |

21 |
Quantum critical lines in holographic phases with (un)broken symmetry,
- Gouteraux, Kiritsis
- 2013
(Show Context)
Citation Context ...or any asymptotically locally Lifshitz background, with or without hyperscaling violation, and for any values of the dynamical exponents z and θ, as well as the vector hyperscaling violating exponent =-=[1]-=-, that are compatible with the null energy condition. The analysis is carried out for a very general bottom up model of gravity coupled to a massive vector field and a dilaton with arbitrary scalar co... |

20 | Holographic Entanglement Entropy and Fermi - Shaghoulian |

20 | Holographic renormalization as a canonical transformation - Papadimitriou - 2010 |

19 |
Thermodynamics of asymptotically locally
- Papadimitriou, Skenderis
(Show Context)
Citation Context ...ovides the necessary local boundary counterterms to render the on-shell action finite, but also is required in order for the variational problem to be well defined both for asymptotically locally AdS =-=[46]-=- and asymptotically non AdS [45] backgrounds. Moreover, the procedure of holographic renormalization based on such an asymptotic solution of the HJ equation is completely equivalent to the traditional... |

17 | Anomalous Breaking of Anisotropic Scaling - Baggio, Boer, et al. |

16 | Hamilton-Jacobi renormalization for Lifshitz spacetime,
- Baggio, Boer, et al.
- 2012
(Show Context)
Citation Context ...ned in order to obtain an exact background solution. Backgrounds with w̃n = 0 can be obtained through the recursion relations (3.58) applied to any n > 2. These results are in agreement with those of =-=[1, 27, 31]-=-, which were obtained through an analysis of the linearized fluctuations of the equations of motion. Here we have derived these in a simpler way using only the superpotential equation (3.10). There is... |

16 | Lecture notes on holographic renormalization,” Class.Quant.Grav - Skenderis |

15 | Holographic Renormalization for z=2 Lifshitz Space-Times from AdS”,
- Chemissany, Geissbuhler, et al.
- 2012
(Show Context)
Citation Context ... = 2 Lifshitz backgrounds are obtained from the reduction of 5-dimensional Schrödinger solutions of the axion-dilaton theory with z = 0, which are asymptotically AdS5. This connection was utilized in =-=[36]-=- in order to deduce the holographic dictionary for the Lifshitz backgrounds from the dictionary for asymptotically locally AdS solutions of the axion-dilaton theory developed in [37]. The same model w... |

14 | Melby-Thompson, “Lifshitz Gravity for Lifshitz Holography - Griffin, Horava, et al. |

12 |
Canonical variables for general relativity.
- Arnowitt, Deser, et al.
- 1960
(Show Context)
Citation Context ...or the action (2.6) is a radial Hamiltonian description of the dynamics, where the radial coordinate is interpreted as the Hamiltonian ‘time’. We start by the standard ADM decomposition of the metric =-=[50]-=- as ds2 = (N2 +NiN i)dr2 + 2Nidrdx i + γij(r, x)dx idxj , (2.10) where N and Ni are respectively the shift and lapse functions, and γij is the induced metric on the radial slices Σr. In terms of these... |

11 |
The domain wall
- Boonstra, Skenderis, et al.
- 1999
(Show Context)
Citation Context ...(3.18). The resulting family of solutions with parameters d = p, z = 1, αξ = 4(p− 1)(4− p) (7− p)2 , ξ = 2(p− 3) p(7− p) , µ = (7− p)(p− 3) 2(5− p) , (3.25) corresponds to Dp branes in the dual frame =-=[15, 16]-=-. 3.3 hvLf solutions By means of the coordinate transformation u = |θ| d r d θ , θ 6= 0, (3.26) and a suitable rescaling of the time and spatial coordinates, the hvLf metric (1.1) takes the form ds2 =... |

8 | Generalized dilatation operator method for non-relativistic holography,” arXiv:1405.3965 [hep-th - Chemissany, Papadimitriou |

8 | Holographic Renormalization for Asymptotically - Mann, McNees - 2011 |

7 |
Curvature singularities: The Good, the bad
- Gubser
(Show Context)
Citation Context ...nce this is the proper holographic frame in the case θ 6= 0, there are no restrictions on θ imposed by requiring absence of curvature singularities in the UV. In the IR one can apply the criterion of =-=[23]-=-, which again provides an unambiguous statement about curvature singularities in the presence of scalars. Restrictions on θ and z do arise, however, from the null energy condition (NEC) Tµνk µkν ≥ 0, ... |

6 |
Lifshitz from AdS at finite temperature and top down models,”
- Korovin, Skenderis, et al.
- 2013
(Show Context)
Citation Context ...known subtleties associated with AdS2 holography. Finally, one can study Lifshitz backgrounds with dynamical exponent infinitesimally close to the relativistic value, i.e. z = 1 + , where is small =-=[40, 41]-=-. This corresponds to deforming the relativistic CFT with an irrelevant operator and so the analysis must be done with a UV cut-off. The main goal of the present paper is a systematic derivation of th... |

6 |
xTras: a field-theory inspired xAct package for
- Nutma
(Show Context)
Citation Context ...using the integration technique developed in [37]. Solving the HJ equation then becomes entirely algorithmic and it is ideally suited for implementation in a symbolic computation package such as xAct =-=[60]-=-. The recursion relations (4.84), (4.85) and (4.86) are identical in form to the equations appearing in the recursive solution of the HJ equation for relativistic backgrounds [37] and exactly the same... |

4 | Lifshitz as a deformation of anti-de Sitter,
- Korovin, Skenderis, et al.
- 2013
(Show Context)
Citation Context ...known subtleties associated with AdS2 holography. Finally, one can study Lifshitz backgrounds with dynamical exponent infinitesimally close to the relativistic value, i.e. z = 1 + , where is small =-=[40, 41]-=-. This corresponds to deforming the relativistic CFT with an irrelevant operator and so the analysis must be done with a UV cut-off. The main goal of the present paper is a systematic derivation of th... |

3 | et al., “Bianchi Attractors: A - Iizuka, Kachru, et al. |

3 | Riccati equations for holographic 2-point functions
- Papadimitriou, Taliotis
(Show Context)
Citation Context ...without any need for solving the second order equations of motion. In fact, the Hamilton-Jacobi equation leads to a much more efficient method for computing renormalized correlation functions as well =-=[52, 61, 62]-=-. Our method provides a solid basis for computing correlation functions in asymptotically Lifshitz and hyperscaling violating Lifshitz backgrounds, and we intend to explore this direction in future wo... |

3 | On the Hamilton-Jacobi equation for second-class constrained systems - Rothe, Scholtz |

2 | On hvLif-like solutions in gauged Supergravity - Bueno, Chemissany, et al. |

2 | Hamilton-Jacobi quantization of a free particle on a (n-1) sphere - Hong, Rothe |

1 | nonconformal field theories and brane - Gherghetta, Oz, et al. |

1 | Holographic renormalization for coincident Dp-branes, JHEP 0810 - Wiseman, Withers - 2008 |

1 | AdS null deformations with inhomogeneities - Narayan |