Seiberg-Witten period relations in Omega background

TL;DR

This paper extends Seiberg-Witten theory by formulating discretised period relations within the Omega background using qq-characters and differential forms, providing new tools for understanding gauge theories.

Contribution

It introduces discretised Seiberg-Witten period relations in the Omega background through novel differential forms and qq-characters, advancing the mathematical framework of gauge theories.

Findings

Discretised Seiberg-Witten period relations established

Differential forms acting on Young diagram space defined

New relations for the prepotential derived

Abstract

Omega-deformation of the Seiberg-Witten curve is known to be written in terms of the qq-character, namely the trace of a specific operator acting in a Hilbert space spanned by certain Young diagrams. We define a differential form acting on this space and establish two discretised versions of the Seiberg-Witten expressions for the periods and related relations for the prepotential.