Correspondences between WZNW models and CFTs with W-algebra symmetry

2019

J. High Energ. Phys.

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193

We analyze the asymptotic symmetry of higher spin gravity with M × M matrix valued fields, which is given by rectangular W-algebras with su(M ) symmetry. The matrix valued extension is expected to be useful for the relation between higher spin gravity and string theory. With the truncation of spin as s = 2, 3, . . . , n, we evaluate the central charge c of the algebra and the level k of the affine currents with finite c, k. For the simplest case with n = 2, we obtain the operator product expansions among generators by requiring their associativity. We conjecture that the symmetry is the same as that of Grassmannian-like coset based on our proposal of higher spin holography. Comparing c, k from the both theories, we obtain the map of parameters. We explicitly construct low spin generators from the coset theory, and, in particular, we reproduce the operator product expansions of the rectangular W-algebra for n = 2. We interpret the map of parameters by decomposing the algebra in the coset description.

“…We begin with the simplest case with n = 2. We consider the sl(2M ) WZNW model with the level t. The reduction procedure in [45] (see also [46][47][48]) would lead to the action…”

Section: Actions For Rectangular W-algebrasmentioning

confidence: 99%

Rectangular W-algebras, extended higher spin gravity and dual coset CFTs

Creutzig

2019

J. High Energ. Phys.

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193

“…The method was used to re-derive (generalized) Ribault-Teschner relation [20,22]. See [23][24][25][26] for extensions of the work. We first consider the Riemann surface of sphere topology and then generalize the analysis for higher genus surface.…”

Section: Jhep09(2020)157mentioning

confidence: 99%

Correlation functions of symmetric orbifold from AdS3 string theory

Liu

2020

J. High Energ. Phys.

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The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The radius of AdS3 is related to the level k of the WZNW model. For k = 3, our result should be an important ingredient for deriving AdS3/CFT2 correspondence with tensionless superstrings to all orders in string perturbation theory. For generic k, relations involving specific forms of correlation functions for strings on AdS3× X were obtained.

“…The degenerate representations of the W-algebra may be examined from those of sl (4) Wess-Zumino-Novikov-Witten (WZNW) model by applying the Hamiltonian reduction. As argued in [2], we may study the Hamiltonian reduction by following the procedure of [30] (see also [31,32,33]). It is convenient to use the description of sl(4) WZNW model as (see (4.6) of [30])…”

Section: Hamiltonian Reduction Of Sl(4)mentioning

confidence: 99%

Rectangular W algebras and superalgebras and their representations

Creutzig

2019

Phys. Rev. D

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We study W-algebras obtained by quantum Hamiltonian reduction of sl(M n) associated to the sl(2) embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with M × M matrix valued fields. In our previous work, we examined the basic properties of the W-algebra and claimed that the algebra can be realized as the symmetry of Grassmannianlike coset even with finite central charge based on a proposal of holography. In this paper, we extend the analysis in the following ways. Firstly, we compute the operator product expansions among low spin generators removing the restriction of n = 2. Secondly, we investigate the degenerate representations in several ways, and see the relations to the coset spectrum and the conical defect geometry of the higher spin gravity. For these analyses, we mainly set M = n = 2. Finally, we extend the previous analysis by introducing N = 2 supersymmetry. *