Fuzzy Black Holes from Mass Generation in Matrix Compactification

TL;DR

This paper explores how mass terms and fuzzy sphere geometries emerge in matrix theories through compactification and boundary conditions, leading to black hole solutions with entropy from fermionic excitations.

Contribution

It extends a mass generation mechanism to BFSS matrix theory with new boundary conditions, resulting in fuzzy sphere black holes and entropy accounting.

Findings

Mass terms generated via compactification and boundary conditions.

Fuzzy sphere geometries serve as black hole solutions.

Fermionic zero modes explain black hole entropy.

Abstract

We investigate a mechanism for generating mass terms in the IKKT and BFSS matrix theories through compactification on a torus and the derivation of a zero-mode effective theory, emphasising the crucial role of fermionic boundary conditions. Extending a recent proposal developed for the IKKT model to the BFSS framework, we explore a broader class of mixed fermionic boundary conditions in both theories. This choice leads to a distinct effective theory with intermediate features, where a mass term is generated together with fermionic zero modes. In the BFSS case, this setup further allows for the construction of black hole solutions. The resulting geometry takes the form of a fuzzy sphere, with quantum excitations in the fermionic sector accounting for the corresponding black hole entropy.