Strange duality revisited

TL;DR

This paper proves the strange duality of conformal blocks in WZW models for higher genus curves by extending genus-0 results using conformal embedding branching rules, unifying several prior results.

Contribution

It extends the proof of strange duality from genus-0 to higher genus curves using explicit conformal embedding branching rules.

Findings

Proof of strange duality for higher genus curves.

Unification of previous results by Belkale, Marian-Oprea, and Oudompheng.

Explicit use of conformal embedding branching rules.

Abstract

We give a proof of the strange duality or rank-level duality of the WZW models of conformal blocks by extending the genus-0 result, obtained by Nakanishi-Tsuchiya in 1992, to higher genus curves via the sewing procedure. The new ingredient of the proof is an explicit use of the branching rules of the conformal embedding of the affine Lie algebras sl(r) x sl(l) in sl(rl). We recover the strange duality of spaces of generalized theta functions obtained by Belkale, Marian-Oprea, as well as by Oudompheng in the parabolic case.