Webs of Walls

TL;DR

This paper constructs and analyzes webs of domain walls as 1/4 BPS states in supersymmetric gauge theories, explicitly describing their moduli space and solutions, especially in the strong coupling limit.

Contribution

It provides a detailed construction of wall web solutions, identifies their moduli space as a complex Grassmann manifold, and explicitly solves for these configurations in the strong coupling limit.

Findings

Moduli space of wall webs is the complex Grassmann manifold.

Explicit solutions for wall webs are obtained in the strong coupling limit.

Correspondence between wall web configurations and the moduli space CP^{Nf-1} in Abelian theories.

Abstract

Webs of domain walls are constructed as 1/4 BPS states in d=4, N=2 supersymmetric U(Nc) gauge theories with Nf hypermultiplets in the fundamental representation. Web of walls can contain any numbers of external legs and loops like (p,q) string/5-brane webs. We find the moduli space M of a 1/4 BPS equation for wall webs to be the complex Grassmann manifold. When moduli spaces of 1/2 BPS states (parallel walls) and the vacua are removed from M, the non-compact moduli space of genuine 1/4 BPS wall webs is obtained. All the solutions are obtained explicitly and exactly in the strong gauge coupling limit. In the case of Abelian gauge theory, we work out the correspondence between configurations of wall web and the moduli space CP^{Nf-1}.