3D Gravity and Chaos in CFTs with Fermions

TL;DR

This paper develops a fermionic 3D gravity theory with spin structures, linking it to fermionic 2D CFTs, and explores its spectral properties, black hole microstates, and consistency with random matrix theory.

Contribution

It introduces a fermionic 3D gravity model with spin structures and connects it to fermionic 2D CFT data, analyzing spectral statistics and topological effects.

Findings

Fermionic black hole microstates exist without bulk fermionic matter.

Spectral statistics match fermionic 2D CFT anomaly patterns.

A new fermionic RMT framework reproduces gravitational spectral results.

Abstract

Pure 3d gravity in AdS is believed to admit a holographic description in terms of 2d CFT. We introduce a theory of fermionic 3d gravity where we sum over geometries equipped with spin structure, and propose it is holographically described by fermionic 2d CFT data. We evaluate the leading contributions to the gravity path integral with one and two torus boundaries, extracting both the spectrum and its spectral statistics from the torus wormhole. Strikingly, the theory has fermionic black hole microstates, even in the absence of bulk fermionic matter. We then incorporate subtle bulk topological field theories, classified by appropriate cobordism groups, and evaluate the one and two-boundary torus partition functions. The spectral statistics we derive from gravity are shown, in all cases, to be consistent with the pattern of anomalies expected from classifications of fermionic 2d CFT. We also define a version of RMT$_2$, a random-matrix framework compatible with the symmetries of 2d CFTs, which naturally accommodates fermionic spectra and reproduces our gravitational results across all cases we analyze.