Higher spin AdS3 holography with extended supersymmetry

Abstract

We propose a holographic duality between a higher spin AdS 3 gravity with so(p) extended supersymmetry and a large N limit of a 2-dimensional Grassmannian-like model with a specific critical level k = N and a non-diagonal modular invariant. As evidence, we show the match of one-loop partition functions. Moreover, we construct symmetry generators of the coset model for low spins which are dual to gauge fields in the supergravity. Further, we discuss a possible relation to superstring theory by noticing an N = 3 supersymmetry of critical level model at finite k, N . In particular, we examine BPS states and marginal deformations. Inspired by the supergravity side, we also propose and test another large N CFT dual obtained as a Z 2 automorphism truncation of a similar coset model, but at a non-critical level.

$$ \mathcal{N}=\left(3,3\right) $$ holography on AdS3 × (S3 × S3 × S1)/ℤ2

“…This yields the higher spin algebra ho(4|1)[0] in the case of S 0 , which is broken down to ho(3|1)[0] when taking the Z 2 -orbifold. This shows that the higher spin dualities of [36] are not directly embeddable in the stringy duality, similar to what was concluded in the large N = 4 case for the higher spin duality of [31].…”

Higher spin currents in the enhanced N = 3 $$ \mathcal{N}=3 $$ Kazama-Suzuki model

“…corresponding to (3.21) of [18]. We observe that the levels are given by (N +2M ), (2N +M ) and 2N M (N + M ) 2 corresponding to the SU(N ), SU(M ) and U(1) factors appearing on the denominator of the coset (1.1) respectively.…”

“…For the N = 3 holography [18], the deformation breaks the higher spin symmetry and induces the mass to the higher spin fields [19,20]. The masses are not generated for the SO(3) R singlet higher spin fields at the leading order of 1 c while the mass formula for the SO(3) R triplet higher spin fields looks like the Regge trajectory on the flat spacetime.…”

“…Furthermore, by taking one of the spin-1 currents and one of the spin-3 2 currents of N = 2 superconformal algebra and calculating the OPE between them (their SO (3) indices are different from each other), one obtains the first-order pole which provides the spin- 2 ). Therefore, the N = 3 superconformal algebra generated by the currents of spins ( 2 ) and computing the OPEs between them is realized in the enhanced N = 3 Kazama-Suzuki model (1.1) together with (1.2) [18].…”

“…the above coset model (1.1) has N = 3 supersymmetry [18][19][20]. According to the previous analysis, there exist (N +M ) 2 −1 adjoint spin- [21][22][23][24][25][26].…”