Proving the OSV conjecture with the gravitational path integral

@misc{bobev2026proving,
  title = {{Proving the OSV conjecture with the gravitational path integral}},
  author = {Nikolay Bobev and Jan Boruch and Luca V. Iliesiu and Dawid Maskalaniec},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12550},
  eprint = {2610.12550},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12550},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Proving the OSV conjecture with the gravitational path integral
AU  - Nikolay Bobev
AU  - Jan Boruch
AU  - Luca V. Iliesiu
AU  - Dawid Maskalaniec
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12550
UR  - https://arxiv.org/abs/2610.12550
AB  - The OSV conjecture relates the helicity supertrace of black holes in 4d 𝒩=2 supergravity obtained through a Calabi--Yau compactification of Type IIA string theory to the modulus squared of the topological string partition function evaluated at the attractor point in moduli space for a given set of magnetic black hole charges and electric chemical potentials. We find Euclidean black hole saddles that compute this index to all orders in the 4d supergravity derivative expansion and calculate their action using equivariant localization. The gravitational on-shell action localizes entirely to the north and south poles of each black hole, with the two contributions determined by the holomorphic and anti-holomorphic topological string free energies, respectively, evaluated at the attractor values of the moduli. For single-center black hole saddles, this provides a proof of the OSV conjecture to all orders in the topological string coupling. The same localization formula also applies to all saddles that contribute to the helicity supertrace, such as multi-center black holes, which leads to a non-perturbative refinement of the conjecture.
ER  -