# An approach to BPS black hole microstate counting in an N=2 STU model

## TL;DR

This paper develops a microstate counting formula for 4D BPS black holes in an N=2 STU model, using quantum entropy functions and modular forms, revealing connections to integrable models and string web pictures.

## Contribution

It introduces a novel microstate counting approach based on modular forms and explores its relation to Calogero models and string web configurations.

## Key findings

- Microstate counting formula involving Siegel modular forms.
- Connections to rational Calogero model.
- Proposal of a string web interpretation.

## Abstract

We consider four-dimensional dyonic single-center BPS black holes in the $N=2$ STU model of Sen and Vafa. By working in a region of moduli space where the real part of two of the three complex scalars $S, T, U$ are taken to be large, we evaluate the quantum entropy function for these BPS black holes. In this regime, the subleading corrections point to a microstate counting formula partly based on a Siegel modular form of weight two. This is supplemented by another modular object that takes into account the dependence on $Y^0$, a complex scalar field belonging to one of the four off-shell vector multiplets of the underlying supergravity theory. We also observe interesting connections to the rational Calogero model and to formal deformation of a Poisson algebra, and suggest a string web picture of our counting proposal.