The mixed black hole partition function for the STU model

TL;DR

The paper evaluates the mixed partition function for dyonic BPS black holes in the STU model using a recently proposed degeneracy formula expressed through the automorphic form $\Phi_k$ with $k=0$. By assembling three triality-related sectors and performing a saddle-point analysis in the large-charge limit, the authors show that the STU mixed partition function factorizes into the OSV-like mixed partition function multiplied by a universal measure factor, which precisely matches the conjectured $e^{\mathcal{K}}$-type measure. This provides nontrivial evidence for OSV-type relations in a concrete $N=2$ setting and supports the proposed measure for STU, while clarifying domain validity and caveats related to walls of marginal stability and single-centered black holes. The work also contrasts STU with $N=4$ models, noting differences in wall-crossing behavior and emphasizing the need for careful treatment of stability regions in extending these results. Overall, the results reinforce a deep link between microscopic dyon degeneracies, duality-invariant automorphic data, and macroscopic entropy, within a well-defined large-charge regime.

Abstract

We evaluate the mixed partition function for dyonic BPS black holes using the recently proposed degeneracy formula for the STU model. The result factorizes into the OSV mixed partition function times a proportionality factor. The latter is in agreement with the measure factor that was recently conjectured for a class of N=2 black holes that contains the STU model.