A Lorentzian Equivariant Index Theorem
Differential Geometry
2026-02-19 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We develop a formula for the equivariant index of a twisted Dirac operator on a compact globally hyperbolic spacetime with timelike boundary on which a group acts isometrically, subject to APS boundary conditions. The formula is the same as in the Riemannian case: the equivariant index for a group element is an integral over the fixed point set of that element plus some boundary terms. The proof uses a surprisingly simple technique for reducing from the equivariant to the non-equivariant regime in order to show an equivariant version of the Lorentzian "index spectral flow" formula.
Cite
@article{arxiv.2602.16547,
title = {A Lorentzian Equivariant Index Theorem},
author = {Onirban Islam and Lennart Ronge},
journal= {arXiv preprint arXiv:2602.16547},
year = {2026}
}