Minimal model holography

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.

Section: Jhep05(2014)103mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Joung

Mkrtchyan

2014

148

“…Higher spin holography has provided valuable perspective on what kinds of CFTs can be expected to have gravity duals; to boot, there are consistent theories of 3d higher spins that lie on the gravity side of specific duality proposals [9][10][11]. These theories are well-known to present unfamiliar puzzles regarding the roles of spacetime geometry, thermodynamics and gauge invariance.…”

Section: Jhep05(2014)052mentioning

confidence: 99%

“…Our answer will also easily admit an n → 1 limit, which yields spinning primary contributions to entanglement entropy. 11 We use slightly different normalization conventions compared to [30] (they include a factor of the norm, which they call αK ) and [20] (they orthonormalize their operators).…”

Section: Spinning Primaries Revisitedmentioning

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.

“…A covariant version is also possible and is seen to explain [20] some of the interesting one-loop results found in [32,33]. More complex Higher Spin correspondences involving conformal theories in 2d are also of high interest [16,28]. In this paper we aim to strengthen the Collective/Gravity identification and provide deeper understanding of it.…”

Section: Jhep01(2015)055mentioning

confidence: 93%

Holography as a gauge phenomenon in Higher Spin duality

Koch

Jevicki

Rodrigues

et al. 2015

Employing the world line spinning particle picture. We discuss the appearance of several different 'gauges' which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic equivalences between them. For a bulk identification we develop a 'gauge independent' representation where all gauge constraints are eliminated. This 'gauge reduction' of Higher Spin Gravity demonstrates that the physical content of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar field in 6d. It is in this gauge reduced form that HS Theory can be seen to be equivalent to a 3 + 3 dimensional bi-local collective representation of CFT 3 .