Higher spin algebras and large $$ \mathcal{N} $$ = 4 holography

Self Cite

We consider string theory on AdS 3 × (S 3 × S 3 × S 1 )/Z 2 , a background supporting N = (3, 3) spacetime supersymmetry. We propose that string theory on this background is dual to the symmetric product orbifold of S 0 /Z 2 where S 0 is a theory of four free fermions and one free boson. We show that the BPS spectra of the two sides of the duality match precisely. Furthermore, we compute the elliptic genus of the dual CFT and that of the supergravity limit of string theory and demonstrate that they match, hence providing non-trivial support for the holographic proposal.

Section: Jhep07(2018)143 7 Conclusionmentioning

confidence: 99%

“…This N = 2 higher spin algebra is invariant under the Z 2 -orbifold. Another approach was investigated in [35], which breaks all supersymmetry, but keeps the R-symmetry explicit. 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.…”

Section: Jhep07(2018)143 7 Conclusionmentioning

confidence: 99%

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

Eberhardt

Zadeh

2018

Self Cite

“…A partial result for this has been already provided in [13]. It is also of our great interest to introduce supersymmetry to relate superstring theory as in [55,40,56,41,13], see also [57,58]. number RES0019997.…”

Section: Conclusion and Discussionmentioning

confidence: 90%

Correspondences between WZNW models and CFTs with W-algebra symmetry

Creutzig

Hikida

Rønne

2016

Abstract:We study theories with W -algebra symmetries and their relation to WZNWtype models on (super-)groups generalizing the H + 3 WZNW to Liouville correspondence. Correlation functions of the WZNW models are expressed in terms of correlators of CFTs with W -algebra symmetry. The symmetries of the theories involved in these correspondences are related by the Drinfeld-Sokolov reduction of Lie algebras to W -algebras. The W -algebras considered in this paper are the Bershadsky-Polyakov algebra for sl(3) and the quasi-superconformal algebra for generic sl(N |M ). The quantum W -algebras obtained from affine sl(N ) are constructed using embeddings of sl(2) into sl(N ), and these can in turn be characterized by partitions of N . The above cases correspond to N + 2 = 2 + N 1 and its supergroup extension. Finally, sl(2N ) and the correspondence corresponding to 2N = N 2 is also analyzed. These are all W -algebras that are generated by fields of at most dimension two.

“…at a large N limit, see also [5,6,7] for related works. Setting M = 1, the proposal essentially reduces to the Gaberdiel-Gopakumar duality [8] and its N = 2 version becomes the same as that of [9].…”

Section: Introductionmentioning

confidence: 97%

“…As in the bosonic cases, we can construct the restricted matrix extensions of higher spin supergravity with so(M) or sp(2m) symmetry. See [6] for the holography with the higher spin supergravities. Without matrix extensions, the holography with N = 1 truncated higher spin supergravity was proposed in [24] and the quantum asymptotic symmetry was examined in [25].…”

Section: Introductionmentioning

confidence: 99%

Rectangular W-algebras of types so(M) and sp(2M) and dual coset CFTs

Creutzig

Hikida

Uetoko

2019

We examine rectangular W-algebras with so(M ) or sp(2M ) symmetry, which can be realized as the asymptotic symmetry of higher spin gravities with restricted matrix extensions. We compute the central charges of the algebras and the levels of so(M ) or sp(2M ) affine subalgebras by applying the Hamiltonian reductions of so or sp type Lie algebras. For simple cases with generators of spin up to two, we obtain their operator product expansions by requiring the associativity. We further claim that the W-algebras can be realized as the symmetry algebras of dual coset CFTs and provide several strong supports. The analysis can be regarded as a check of extended higher spin holographies including full quantum corrections. We also extend the analysis by introducing N = 1 supersymmetry. *