Global Structure of Moduli Space for BPS Walls

TL;DR

This paper explores the complex global structure of BPS wall moduli spaces in supersymmetric theories, revealing larger-than-expected dimensions, union of special Lagrangian submanifolds, and novel wall dynamics like transmutation and locking.

Contribution

It uncovers the intricate global topology of BPS wall moduli spaces, including their union over multiple submanifolds and novel wall interactions, extending previous understanding of BPS solitons.

Findings

Moduli space dimension can exceed naive index theorem predictions.

Total moduli space is a union of several special Lagrangian submanifolds.

Walls exhibit complex dynamics such as mutual repulsion, attraction, and transmutation.

Abstract

We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold M, and find that the dimension of the moduli space can be larger than that naively suggested by the index theorem, contrary to previous examples of BPS solitons. We investigate BPS wall solutions in an explicit example of M using Abelian gauge theory. Its Higgs branch turns out to contain several special Lagrangian submanifolds including M. We show that the total moduli space of BPS walls is the union of these submanifolds. We also find interesting dynamics between BPS walls as a byproduct of the analysis. Namely, mutual repulsion and attraction between BPS walls sometimes forbid a movement of a wall and lock it in a certain position; we also find that a pair of walls can transmute to another pair of walls with different tension after they pass through.