Computation of the index on orbifold from the Atiyah-Segal-Singer fixed point theorem
Year: 2024
Type: article
Abstract: We investigate the independent chiral zero modes on the orbifolds from the Atiyah-Segal-Singer fixed point theorem. The required information for this calculation includes the fixed points of the orbifold and the manner in which the spatial symmetries act on these points, unlike previous studies that necessitated the calculation of zero modes. Since the fixed point theorem can be applied to any fermionic theory on any orbifold, it allows us to determine the index even on orbifolds where the calculation of zero modes is challenging or in the presence of nontrivial gauge configurations. We compute the indices on the T 2 / Z N ( N = 2 , 3 , 4 , 6 ) and T 4 / Z N ( N = 2 , 3 , 5 ) as examples. Furthermore, we also attempt to compute the indices on a Coxeter orbifold related to the D 4 lattice. Published by the American Physical Society 2024
Authors: Shoto Aoki, Maki Takeuchi
Institutions: The University of Tokyo, Yamaguchi University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4404525709