The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators
Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo, Tetsuya Onogi,, Satoshi Yamaguchi, Mayuko Yamashita
TL;DR
This paper presents a new mathematician-friendly formulation of the Atiyah-Patodi-Singer index, clarifying its relationship with domain-wall fermions and edge modes in a way accessible to mathematicians.
Contribution
It offers a novel, mathematically accessible derivation of the Atiyah-Patodi-Singer index connecting it with domain-wall fermions and boundary phenomena.
Findings
New formulation clarifies the index's relation to boundary conditions.
Provides insights into the interplay between domain-wall fermions and edge modes.
Enhances understanding of the mathematical structure underlying physical boundary phenomena.
Abstract
We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index of our previous paper. Our viewpoint sheds some new light on the interplay among the Atiyah-Patodi-Singer boundary condition, domain-wall fermions, and edge modes.
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