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arXiv · 2602.16547

A Lorentzian Equivariant Index Theorem

Onirban Islam·Lennart Ronge
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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.

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Onirban Islam, Lennart Ronge. 2026-02-18. A Lorentzian Equivariant Index Theorem. https://arxiv.org/abs/2602.16547

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