Seiberg-Witten prepotential from WZNW conformal block: Langlands duality and Selberg trace formula

TL;DR

This paper demonstrates how SU(2) Nf=4 Seiberg-Witten prepotentials can be derived from WZNW conformal blocks using Langlands duality, linking gauge theory and conformal field theory.

Contribution

It introduces a novel approach connecting Seiberg-Witten prepotentials with WZNW conformal blocks through Langlands duality.

Findings

Derived Seiberg-Witten prepotentials from conformal blocks.

Established a connection between gauge theory and conformal field theory.

Utilized Langlands duality in the derivation process.

Abstract

We show how SU(2) $N_f=4$ Seiberg-Witten prepotentials are derived form $\hat{\mathfrak{sl}}_{2,k}$ ($k\to2$) four-point conformal blocks via considering Langlands duality.