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arXiv · 2607.07621

Odd-Dimensional Localization in Supergravity

Pietro Benetti Genolini·Florian Gaar·Jerome P. Gauntlett·Jaeha Park·James Sparks
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Abstract

We establish a localization principle for odd-dimensional supergravity theories containing Chern--Simons interactions. Our construction relies on combining an equivariant extension of the gauge-invariant part of the action with an equivariant completion of the Chern--Simons anomaly form ${\Phi}^{(\text{anom})}$ to form a relative equivariant cohomology class. This leads to a universal fixed point formula for the on-shell action of supersymmetric solutions that is expressed in terms of ${\Phi}^{(\text{anom})}$ and an equivariant Euler class. We illustrate the formalism in $D=11$ and $D=5$ supergravity, with applications including the supersymmetric Casimir energy and superconformal index of M5-branes, as well as black ring and black lens solutions.

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Pietro Benetti Genolini, Florian Gaar, Jerome P. Gauntlett, Jaeha Park, James Sparks. 2026-07-08. Odd-Dimensional Localization in Supergravity. https://arxiv.org/abs/2607.07621

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