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Index Theorem for Domain Walls

A. V. Ivanov

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.

Index Theorem for Domain Walls

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.

Paper Structure

This paper contains 5 sections, 3 theorems, 20 equations.

Table of Contents

  1. Introduction
  2. The main result
  3. Auxiliary lemma
  4. Discussion
  5. Acknowledgements.

Key Result

Theorem 1

Under the conditions described above we have the equalities:

Theorems & Definitions (7)

  • Definition
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • proof