Asymptotic $ \mathcal{W} $ -symmetries in three-dimensional higher-spin gauge theories

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%

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

Joung

Mkrtchyan

2014

148

“…(The precise map beyond low spins is subject to some ambiguities that have yet to be resolved [38].) An important point is that we always demand that our theory contain a metric.…”

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.

“…Next, by using the fifth equation of (C.1) with spin Let us focus on the 1 (z−w) 4 terms in the operator product expansion of W (z)W (w) where the spin 2 current W (z) is the first component of W (Z) in (2.19) that has the form in (2.24) together with (F.1). One determines the overall constant A(k) 25) by requiring that the 1 (z−w) 4 term should be equal to c 2 where the central charge is 10 Totally, there are 249 independent terms if we expand out the structure constants(the number of nonzero structure constants is 492 from the discussion of the Appendix E) and the metric.…”

Section: Thementioning

confidence: 99%

The large N ’t Hooft limit of Kazama-Suzuki model

Ahn

2012

We consider N = 2 Kazama-Suzuki model on CP N = SU (N +1) SU (N )×U (1) . It is known that the N = 2 current algebra for the supersymmetric WZW model, at level k, is a nonlinear algebra. The N = 2 W 3 algebra corresponding to N = 2 was recovered from the generalized GKO coset construction previously. For N = 4, we construct one of the higher spin currents, in N = 2 W 5 algebra, with spins (2, 5 2 , 5 2 , 3). The self-coupling constant in the operator product expansion of this current and itself depends on N as well as k explicitly. We also observe a new higher spin primary current of spins (3, 7 2 , 7 2 , 4). From the behaviors of N = 2, 4 cases, we expect the operator product expansion of the lowest higher spin current and itself in N = 2 W N +1 algebra. By taking the large (N, k) limit on the various operator product expansions in components, we reproduce, at the linear order, the corresponding operator product expansions in N = 2 classical W cl ∞ [λ] algebra which is the asymptotic symmetry of the higher spin AdS 3 supergravity found recently.