Near-extremal hydrodynamics and the holographic product formula

TL;DR

This paper explores the behavior of holographic spectral functions in near-extremal hydrodynamics, revealing factorization properties and providing new numerical insights into low-temperature quasi-normal modes, with implications for IR conformal behavior.

Contribution

It introduces a holographic product formula approach to analyze spectral functions near extremality, demonstrating factorization and extending understanding of IR conformal regimes.

Findings

Spectral functions simplify in the extremal limit.

Factorization extends to near-extremal regimes at leading order.

New numerical results for low-temperature quasi-normal modes.

Abstract

The holographic product formula is used to determine the general form taken by holographic spectral functions in the near-extremal hydrodynamic regime, with energy $\omega$, momentum $k$ and temperature $T$ much smaller than a hard scale $\mu$. The resulting expressions simplify in the extremal limit $T \ll \omega,k\ll \mu$, for which the low-temperature gapless modes and the IR conformal behavior factorize. In some cases, this factorization extends to the general near-extremal regime $\omega,k,T\ll\mu$ at leading order in $T/\mu$. Several examples are discussed with different types of gapless modes and IR CFTs, including new numerical results for low temperature quasi-normal modes. We end with a concrete application that shows how the inclusion of the IR conformal behavior improves the description of the spectral function at low energies.