A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs

TL;DR

This paper constructs a new class of non-unitary 2D RCFTs with modular data matching Haagerup-Izumi, linking them to 3D non-unitary topological theories derived from S-fold SCFTs, and explicitly computes their characters.

Contribution

It introduces non-unitary RCFTs with Haagerup-Izumi modular data and connects them to 3D non-unitary topological theories from S-fold SCFTs, providing explicit character representations.

Findings

Constructed non-unitary RCFTs with Haagerup-Izumi modular data.

Linked 2D RCFTs to 3D non-unitary topological theories.

Explicitly derived conformal characters using Nahm and Bantay-Gannon methods.

Abstract

We introduce a novel class of two-dimensional non-unitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized Haagerup-Izumi modular data. Via the bulk-boundary correspondence, they are related to the three-dimensional non-unitary Haagerup topological field theories, recently constructed by a topological twisting of three-dimensional ${\cal N}=4$ rank-zero superconformal field theories (SCFTs), called S-fold SCFTs. We propose that, up to the overall factors, the half-indices of the rank-zero SCFTs give the explicit Nahm representation of four conformal characters of the RCFTs including the vacuum character. Using the theory of Bantay-Gannon, we can successfully complete them into the full admissible conformal characters of the RCFTs.