The Witten Index of massless $(d+1)$-Dirac-Schrödinger Operators

Abstract

We calculate the Witten index of a class of (non-Fredholm) Dirac-Schrödinger operators over ${\mathbb{R}}^{d+1}$ for $d\ge 3$ odd, and thus generalize known results for the case $d=1$. For a concrete example of the potential, we give a more explicit index formula, showing that the Witten index assumes any real number on this class of operators.