Review of the holographic Lifshitz theory

Park, Chanyong

doi:10.1142/s0217751x1430049x

Cited by 10 publications

(11 citation statements)

References 50 publications

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“…where φ andã i represent a dilaton and two axion fields and L is the AdS radius. Following the AdS/CFT correspondence, the profile of the dilaton field can be reinterpreted as a nontrivial running scaling [32,33,51,35,52,37], while the bulk gauge field describes a certain fermionic matter like quark [38]. This means that the gravity theory we consider mimics a nonconformal medium composed of fermions and gauge bosons [39,40].…”

Section: Einstein-maxwell-dilaton-axion Modelmentioning

confidence: 99%

Conductivities in an anisotropic medium

2016

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In order to imitate anisotropic medium of a condensed matter system, we take into account an Einstein-Maxwell-dilaton-axion model as a dual gravity theory where the anisotropy is caused by different momentum relaxations. This gravity model allows an anisotropic charged black hole solution. On this background, we investigate how the linear responses of vector modes like electric, thermoelectric, and thermal conductivities rely on the anisotropy. We find that the electric conductivity in low frequency limit shows a Drude peak and that in the intermediate frequency regime it reveals the power law behavior. Especially, when the anisotropy increases the exponent of the power law becomes smaller. In addition, we find that there exist a critical value for the anisotropy at which the DC conductivity reaches to its maximum value.Comment: 23 pages, 9 figure

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Section: Einstein-maxwell-dilaton-axion Modelmentioning

confidence: 99%

Conductivities in an anisotropic medium

2016

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Section: Introductionmentioning

confidence: 99%

“…Motivated by * Electronic address: wbrenna@uwaterloo.ca † Electronic address: rbmann@uwaterloo.ca ‡ Electronic address: miokpark@kias.re.kr the hope of obtaining a duality between condensed matter physics with quantum criticality, the anisotropic scaling properties of these systems imply from gauge-gravity duality that the bulk spacetime geometry likewise asymptotes to a spacetime with the same scaling properties [42]. Known as Lifshitz spacetimes, they remain a subject of intensive study [43][44][45][46].We seek to understand the thermodynamics of Lifshitz black holes [47][48][49] in the context of extended phase space, particularly the notion of mass as enthalpy [13]. Mass, a difficult concept to define in general relativity, is even more problematic when higher-curvature and/or differing asymptotics are incorporated.…”

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confidence: 99%

Mass and thermodynamic volume in Lifshitz spacetimes

2015

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We examine the concept of black hole thermodynamic volume and its consistency with thermodynamic mass in spacetimes that are not asymptotically flat but instead have anisotropic Lifshitz scaling symmetry. We find that the generalized Smarr relation in anti de Sitter spaceextended to include a pressure-volume term -holds here as well, and that there exists a definition of thermodynamic mass and thermodynamic volume that satisfy both this relation and the 1 st law of thermodynamics. We compare the thermodynamic mass with other known quantities such as Arnowitt-Deser-Misner, Brown-York and Hollands-Ishibashi-Marolf masses. We also conjecture methods for obtaining a thermodynamic mass where there is ambiguity due to the cosmological constant lengthscale depending on the horizon radius lengthscale. I. BACKGROUNDGauge-gravity duality remains a subject of considerable interest, in large part because of the insights it yields into quantum gravity. Asymptotically anti de Sitter (AdS) spacetime admits a strongly coupled gauge theory description at its boundary via a holographic dictionary. It is straightforward to define thermodynamic equilibrium in this case, in turn giving rise to thermal radiation/large AdS black hole phase transitions [1].An interesting development in this subject that has been the subject of much current interest is the proposal that the mass of an AdS black hole can be understood as the enthalpy of spacetime [2]. This notion emerges from regarding the cosmological constant Λ as a thermodynamic variable [3] analogous to pressure in the first law [2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], along with a notion of conjugate volume [2,12]. A complete analogy between 4-dimensional Reissner-Nordström AdS black holes and the Van der Waals liquid-gas system can be shown to hold [13]. The critical exponents are the same as those in the Van der Waals system, modifying previous considerations that emerged from earlier studies [19][20][21][22] of the duality description. Intensive investigation in a broad variety of contexts [23-37] has led to the discovery of a variety of new thermodynamic phenomena for both AdS and de Sitter [38] black holes, including the existence of reentrant phase transitions in Born-Infeld [14] and rotating [39] black holes, the existence of a tricritical point in rotating black holes analogous to the triple point in water [39], a new type of thermodynamic criticality in the highercurvature case [40], and the notion of a holographic heat engine [37, 41]. Indeed, the thermal radiation/large AdS black hole phase transition [1] can be understood as a solid/liquid phase transition from this perspective [34].Here we begin the first study of extended thermodynamics in the context of Lifshitz duality. Motivated by * Electronic address: wbrenna@uwaterloo.ca † Electronic address: rbmann@uwaterloo.ca ‡ Electronic address: miokpark@kias.re.kr the hope of obtaining a duality between condensed matter physics with quantum criticality, the anisotropic scaling properties of these systems im...

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“…When one applies the holographic renormalization technique to the gravity with some matter fields, it was shown that there can exist an ambiguity in choosing the counterterms [38,39]. In the holographic Lifshitz theory, for example, there are many different counterterms giving the same UV divergence.…”

Section: Introductionmentioning

confidence: 99%

Holographic RG flow triggered by a classically marginal operator

Park

2021

Preprint

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We study the holographic renormalization group (RG) flow triggered by a classically marginal operator. When a marginal operator deforms a conformal field theory, it does not yield a nontrivial renormalization group flow at the classical level. At the quantum level, however, quantum corrections modify a marginal operator into one of the truly marginal, marginally relevant, and marginally irrelevant operators and can generate a nontrivial RG flow. We investigate the holographic description of a RG flow triggered by a marginal operator with quantum corrections. We look into how the physical quantities of a deformed theory, a coupling constant and the vacuum expectation value, rely on the RG scale. We further discuss the holographic description of the trace anomaly caused by the gluon condensation.

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Review of the holographic Lifshitz theory

Cited by 10 publications

References 50 publications

Conductivities in an anisotropic medium

Conductivities in an anisotropic medium

Mass and thermodynamic volume in Lifshitz spacetimes

Holographic RG flow triggered by a classically marginal operator

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