Ray–Singer torsion, topological strings, and black holes

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Abstract
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 \mathcal {N}=2 supergravity theories.
Funding Information
  • Simons Foundation (602883)
  • Simons Foundation (CV)
  • Simons Foundation (PHY-2013858)
  • National Science Foundation (602883)
  • National Science Foundation (CV)
  • National Science Foundation (PHY-2013858)

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