An analytical approach to the equivariant index and Witten genus on spin manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:164

Article

Villarreal, Juan Jose¹ 

[1] Virginia Commonwealth Univ, Richmond, VA 23284 USA

关键词: Witten genus;    Atiyah-Singer index;    Equivariant index;   

DOI  :  10.1016/j.geomphys.2021.104170

来源: Elsevier

【 摘 要 】

This work is divided in two cases. In the first case, we consider a spin manifold M as the set of fixed points of an S-1-action on a spin manifold X, and in the second case we consider the spin manifold M as the set of fixed points of an S-1-action on the loop space of M. For each case, we build on M a vector bundle, a connection and a set of bundle endomorphisms. These objects are used to build global operators on M which define an analytical index in each case. In the first case, the analytical index is equal to the topological equivariant Atiyah-Singer index, and in the second case the analytical index is equal to a topological expression where the Witten genus appears. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free