Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

148

The higher-spin (HS) algebras relevant to Vasiliev's equations in various dimensions can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebra and consider the corresponding HS algebras. For sp 2N and so N , the minimal representations are unique so we get unique HS algebras. For sl N , the minimal representation has one-parameter family, so does the corresponding HS algebra. The so N HS algebra is what underlies the Vasiliev theory while the sl 2 one coincides with the 3D HS algebra hs [λ]. Finally, we derive the explicit expression of the structure constant of these algebras -more precisely, their bilinear and trilinear forms. Several consistency checks are carried out for our results.

“…In case of slN ⊕ slN Chern-Simons theory, the asymptotic symmetry is given by WN ⊕ WN [21]. Interestingly, WN does not contain slN as subalgebra -at least, not manifestly.…”

Section: Hs Algebras and Reductive Dual Pairsmentioning

confidence: 99%

Notes on higher-spin algebras: minimal representations and structure constants

Joung

Mkrtchyan

2014

148

“…the full higher spin conformal algebra [34][35][36]. The generators of G, which we label V s n , are identified with the wedge modes J (s) n , with |n| < s, and the level k is proportional to the CFT central charge c = 3 /2G.…”

Section: Jhep05(2014)052mentioning

confidence: 99%

Comments on Rényi entropy in AdS3/CFT2

Perlmutter

2014

Abstract:We extend and refine recent results on Rényi entropy in two-dimensional conformal field theories at large central charge. To do so, we examine the effects of higher spin symmetry and of allowing unequal left and right central charges, at leading and subleading order in large total central charge. The result is a straightforward generalization of previously derived formulae, supported by both gravity and CFT arguments. The preceding statements pertain to CFTs in the ground state, or on a circle at unequal left-and right-moving temperatures. For the case of two short intervals in a CFT ground state, we derive certain universal contributions to Rényi and entanglement entropy from Virasoro primaries of arbitrary scaling weights, to leading and next-to-leading order in the interval size; this result applies to any CFT. When these primaries are higher spin currents, such terms are placed in one-to-one correspondence with terms in the bulk 1-loop determinants for higher spin gauge fields propagating on handlebody geometries.

“…The complexity of higher spin theories reduces drastically in three dimensions wherein it becomes possible to consistently truncate to a finite set of higher spin fields [17] and reformulate the theory with spin s ≤ N in terms of SL(N, R) × SL(N, R) Chern-Simons theory [18,19,20,21,22,23,24]. The works of [23,24] have shown that the asymptotic symmetry algebra of such higher spin theories on AdS 3 is (two copies of) the W N algebra.…”

Section: Introductionmentioning

confidence: 99%

“…The works of [23,24] have shown that the asymptotic symmetry algebra of such higher spin theories on AdS 3 is (two copies of) the W N algebra. This naturally generalizes the formulation of ordinary gravity on AdS 3 in terms of SL(2, R) × SL(2, R) Chern-Simons theory [25,26] and extends the associated asymptotic Virasoro symmetry [27] to the W N algebra.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of higher spin black holes in 3D

David

Ferlaino

Kumar

2012

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.