Abstract
We study the index of 4d Yang-Mills theory with gauge group, focusing on the physics of the dual Bogomolny-Prasad-Sommerfield black holes in . Certain aspects of these black holes can be studied from finite indices with reasonably large . We make numerical studies of the index for , by expanding it up to reasonably high orders in the fugacity. The entropy of the index agrees very well with the Bekenstein-Hawking entropy of the dual black holes, say at or 36. Our data clarifies and supports the recent ideas which allowed analytic studies of these black holes from the index, such as the complex saddle points of the Legendre transformation and the oscillating signs in the index. In particular, the complex saddle points naturally explain the -subleading oscillating patterns of the index. We also illustrate the universality of our ideas by studying a model given by the inverse of the MacMahon function.
- Received 23 February 2021
- Accepted 27 April 2021
DOI:https://doi.org/10.1103/PhysRevD.103.126006
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society