The gravitational index and allowable complex metrics
Abstract
We study the Kontsevich-Segal-Witten criterion for allowable complex metrics, in the context of the gravitational path integral corresponding to the supersymmetric index. In various theories of supergravity in asymptotically flat and asymptotically AdS space, the exponential growth of states of the corresponding microscopic index in string theory is known to be captured by complex saddle points of this path integral. We compare the KSW criterion for these complex saddles against constraints from geometric consistency and the convergence of microscopic indices for the same saddles. In all the situations we consider, we find that the three criteria precisely agree with each other.
Cite
@article{arxiv.2503.20866,
title = {The gravitational index and allowable complex metrics},
author = {Pietro Benetti Genolini and Sameer Murthy},
journal= {arXiv preprint arXiv:2503.20866},
year = {2026}
}
Comments
Invited research article for Journal of Physics A Special issue on Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser; v2: 27 pages, section 7 of v1 (on AAdS_5 black holes) has been removed and is superseded by new paper with Oliver Janssen