The Shapes of Dirichlet Defects

TL;DR

This paper numerically analyzes the shapes and intersection regions of topological defects in field theories, revealing complex structures where defects of different dimensions terminate on each other, with implications across physics.

Contribution

It provides a detailed numerical study of the shapes and intersections of topological defects, including walls and strings, in various field theories, connecting to broader physical contexts.

Findings

Walls can terminate on other walls and strings.

Intersection regions of defects exhibit complex structures.

Connections to supersymmetric theories and condensed matter systems.

Abstract

If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher dimension. The shapes of such defects are analyzed numerically, with special attention paid to the intersection regions. Walls (co-dimension 1 branes) terminating on other walls, global strings (co-dimension 2 branes) and local strings (including gauge fields) terminating on walls are all considered. Connections to supersymmetric field theories, string theory and condensed matter systems are pointed out.