The Schwarzian from gauge theories

TL;DR

This paper explores the emergence of the Schwarzian action in gauge theories via holography, connecting low-temperature gravitational dynamics with field theory, and discusses implications for black hole physics and chaos.

Contribution

It demonstrates how the Schwarzian contribution arises from gauge theories and relates to black hole thermodynamics, providing a new perspective on low-temperature expansions and chaos emergence.

Findings

Recovered the Schwarzian contribution at low temperatures.

Matched mass-gap results with supergravity predictions.

Linked reparameterizations to cutoff scale redefinitions.

Abstract

The continuum of holographic dual gravitational charges is recovered out of the discrete spectrum of $U(N)$ $\mathcal{N}=4$ SYM on $\mathbb{R}\times S^3\,$. In such a limit, the free energy of the free gauge theory is computed up to logarithmic contributions and exponentially suppressed contributions. Assuming the supergravity dual prediction to correctly capture strong-coupling results in field theory, the answer is bound to encode a complete low-temperature expansion of the Gibbons-Hawking gravitational on-shell action, valid well beyond the vicinity of supersymmetric black hole solutions. The formula recovers the long awaited Schwarzian contribution at low enough temperatures for certain choices of flows to the continuum. One such choice identifies the chemical potentials and thermodynamic charges in field theory with the chemical potentials and thermodynamic charges of the dual black holes. For such a flow the computed mass-gap kinematically matches the conjectured strong-coupling result obtained by Boruch, Heydeman, Iliesiu and Turiaci in supergravity, including small $1/\lambda$-corrections. The {emergent} reparameterizations, broken by the selection of the Schwarzian, correspond to redefinitions of the relevant cutoff scale. Observations are made regarding the existence of $\frac{1}{8}$-BPS black holes and how this is in tension with BPS inequalities. The RG-flow procedure leading to these results opens a way to understanding the emergence of chaos in gauge theories and its relation to non-extremal and non-supersymmetric black hole physics.