Conformal embeddings and higher-spin bulk duals

TL;DR

This paper explores the construction of higher-spin bulk duals for non-diagonal modular invariants in coset conformal field theories, revealing supersymmetric duals and dualities between different coset models.

Contribution

It systematically identifies higher-spin bulk duals for non-diagonal invariants, including supersymmetric cases, and proposes dualities between different coset CFTs.

Findings

A class of partition functions with enhanced supersymmetry at special 't Hooft couplings

Existence of a $ ext{N}=1$ supersymmetric higher-spin bulk dual for an orthogonal group coset

Duality between different coset models generalizing the 3-state Potts model interpretation

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.