Conformal embeddings and higher-spin bulk duals

Abstract

It is well-known that conformal embeddings can be used to construct non-diagonal modular invariants for affine lie algebras. This idea can be extended to construct infinite series of non-diagonal modular invariants for coset CFTs. In this paper, we systematically approach the problem of identifying higher-spin bulk duals for these kind of non-diagonal invariants. In particular, for a special value of the 't Hooft coupling, there exist a class of partition functions that have enhanced supersymmetry, which should be reflected in a bulk dual. As a illustration of this, we show that a partition function of a orthogonal group coset CFT has a $\mathcal{N}=1$ supersymmetric higher-spin bulk dual, in the 't Hooft limit. We also propose that two of the series of CFT partition functions, obtained from conformal embeddings, are equal, generalising the well-known dual interpretation of the 3-state Potts model as a $\frac{SU(2{)}_3\otimes SU(2{)}_1}{SU(2{)}_4}$ and also as a $\frac{SU(3{)}_1\otimes SU(3{)}_1}{SU(3{)}_2}$ coset model.

arXiv comment40 pages, 1 figure, Version to appear in Physical Review D

References in corpus (24)

• W-symmetry in Conformal Field Theory
• An AdS_3 Dual for Minimal Model CFTs
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Minimal Model Holography
• Higher Spins & Strings
• Partition Functions of Holographic Minimal Models
• The Large N 't Hooft Limit of Coset Minimal Models
• String Theory as a Higher Spin Theory
• Minimal Model Holography for SO(2N)
• The semiclassical limit of W_N CFTs and Vasiliev theory
• Extended higher spin holography and Grassmannian models
• Higher spin AdS_3 holography with extended supersymmetry
• N=1 supersymmetric higher spin holography on AdS_3
• Even spin minimal model holography
• N=1 extension of minimal model holography
• On the coset duals of extended higher spin theories
• Conical Defects in Higher Spin Theories
• The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models
• The $\mathcal{N}=1$ algebra ${\mathcal{W}}_{\infty }[\mu ]$ and its truncations
• On the Classification of Diagonal Coset Modular Invariants
• Higher Spin Currents in Orthogonal Wolf Space
• The W_N minimal model classification
• Quasi-Galois Symmetries of the Modular S-Matrix
• A Unified Scheme for Modular Invariant Partition Functions of WZW Models

Cited by in corpus (5)

• Instanton R-matrix and W-symmetry
• Even spin $\mathcal{N}=4$ holography
• Symmetry Algebras of Stringy Cosets
• Higher Spin Currents in the Orthogonal Coset Theory
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model