Index Theorem for Domain Walls

TL;DR

This paper extends the index theorem for domain walls to include cases where both Yang-Mills and Riemannian connection components jump across a surface, with a continuous metric, broadening the theorem's applicability.

Contribution

The paper introduces an extension of the index theorem to scenarios with simultaneous jumps in Yang-Mills and Riemannian connections across domain walls.

Findings

Extended index theorem applicable to combined Yang-Mills and Riemannian jumps

Applicable to domain walls with continuous metrics

Broadens mathematical understanding of gauge and geometric structures

Abstract

The paper is devoted to the discussion of index theorem for domain walls condition. We give an extension of the theorem to the case, when not only Yang-Mills connection components have a jump on some surface of co-dimension 1, but also components of a Riemannian connection, while a metric remains continuous.