Holographic dual of free field theory

103

Abstract:We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) × SL(3, R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W 3 × W 3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS 3 backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W (2) 3 × W (2) 3 symmetry deformed by a spin-3 2 current. This allows to identify the precise map between UV and IR thermodynamic variables. We find that the high temperature regime is dominated by a black hole branch whose thermodynamics can only be consistently inferred with reference to this W (2) 3 × W (2) 3 CFT.

mentioning

confidence: 46%

Thermodynamics of higher spin black holes in 3D

David

Ferlaino

Kumar

2012

103

“…. ), we can now rewrite (3.35) as 8) where the left hand side is to be understood as a generating function. Next we repeat the argument of [54, p. 40-41].…”

Section: Discussionmentioning

confidence: 99%

“…This offers the hope of finding simplified versions of the AdS/CFT duality. It may also open the way towards a proof of the AdS/CFT correspondence, at least in a specific regime; for first attempts in this direction see [7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric holography on AdS3

Candu

Gaberdiel

2013

161

“…For other holographic approaches to the vector models and related conjectures see refs. [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. We write the partition function as…”

Section: Jhep09(2016)044mentioning

confidence: 99%

Horizon as critical phenomenon

Lee

2016

We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U(N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.