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.

40 pages, 1 figure, Version to appear in Physical Review D