Localization Method for Volume of Domain-Wall Moduli Spaces

TL;DR

This paper derives an exact formula for the volume of moduli spaces of non-Abelian BPS domain-walls and vortices in gauge theories, revealing dualities and geometric properties without explicit metrics.

Contribution

It introduces a novel localization-based method to compute moduli space volumes, establishing dualities and geometric insights in non-Abelian gauge theories.

Findings

Exact volume formula for non-Abelian BPS domain-wall moduli spaces

Identification of Seiberg-like duality between moduli spaces

Discovery of T-duality between domain-walls and vortices

Abstract

Volume of moduli space of non-Abelian BPS domain-walls is exactly obtained in U(N_c) gauge theory with N_f matters. The volume of the moduli space is formulated, without an explicit metric, by a path integral under constraints on BPS equations. The path integral over fields reduces to a finite dimensional contour integral by a localization mechanism. Our volume formula satisfies a Seiberg like duality between moduli spaces of the U(N_c) and U(N_f-N_c) non-Abelian BPS domain-walls in a strong coupling region. We also find a T-duality between domain-walls and vortices on a cylinder. The moduli space volume of non-Abelian local (N_c=N_f) vortices on the cylinder agrees exactly with that on a sphere. The volume formula reveals various geometrical properties of the moduli space.