Small Black holes vs horizonless solutions in AdS

TL;DR

This paper discusses how smooth horizonless geometries can serve as the macroscopic description of certain BPS operators in 4D ${ m N}=1$ toric gauge theories, emphasizing different ensemble perspectives.

Contribution

It introduces a geometric quantization approach for horizonless configurations as a macroscopic description of BPS operators in toric gauge theories.

Findings

Horizonless configurations correspond to microstates in Lorentzian ensembles.

Different ensemble descriptions (Lorentzian vs Euclidean) are crucial for understanding the physics.

Geometric quantization provides a bridge between microstates and semiclassical saddle points.

Abstract

It is argued that the appropriate macroscopic description of half-BPS mesonic chiral operators in generic $d=4$ ${\cal N}=1$ toric gauge theories is in terms of the geometric quantization of smooth horizonless configurations. The relevance of different ensemble macroscopic descriptions is emphasized : lorentzian vs euclidean configurations as (semiclassical) microstates vs saddle points in an euclidean path integral.