Ray-Singer Torsion, Topological Strings and Black Holes

Genus one amplitude for topological strings on Calabi-Yau 3-folds can be computed using mirror symmetry: The partition function at genus one gets mapped to a holomorphic version of Ray-Singer torsion on the mirror Calabi-Yau. On the other hand it can be shown by a physical argument that this gives a curvature squared correction term to the gravitational action. This in paticular leads to an effective quantum gravity cutoff known as the species scale, which varies over moduli space of Calabi-Yau manifolds. This resolves some of the puzzles associated to the entropy of small black holes when there are a large number of light species of particles. Thus Ray-Singer torsion, via its connection to topological strings at genus one, provides a measure of light degrees of freedom of four dimensional N=2 supergravity theories. Based on a talk given on May 12th, 2023 at the Singer Memorial Conference, MIT.