N-point and higher-genus osp(1|2) fusion

TL;DR

This paper investigates the complex fusion processes in affine osp(1|2) conformal field theory, extending methods from affine su(2) fusion to higher-point and higher-genus cases, with explicit formulas for fusion multiplicities.

Contribution

It introduces a novel approach to compute higher-point and higher-genus fusion multiplicities in osp(1|2) using generalized Berenstein-Zelevinsky triangles and virtual couplings.

Findings

Fusion multiplicities are expressed as discretized volumes of convex polytopes.

Explicit multiple sum formulas for fusion multiplicities are provided.

Methods extend previous affine su(2) fusion techniques to osp(1|2).

Abstract

We study affine osp(1|2) fusion, the fusion in osp(1|2) conformal field theory, for example. Higher-point and higher-genus fusion is discussed. The fusion multiplicities are characterized as discretized volumes of certain convex polytopes, and are written explicitly as multiple sums measuring those volumes. We extend recent methods developed to treat affine su(2) fusion. They are based on the concept of generalized Berenstein-Zelevinsky triangles and virtual couplings. Higher-point tensor products of finite-dimensional irreducible osp(1|2) representations are also considered. The associated multiplicities are computed and written as multiple sums.