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One-loop Corrected Holographic Shear Viscosity to Entropy Density Ratio at Low Temperatures

Leopoldo A. Pando Zayas, Jingchao Zhang

TL;DR

The paper addresses how quantum fluctuations in the near-horizon $AdS_2$ throat of near-extremal $AdS_4$ black branes affect holographic transport, focusing on the shear viscosity to entropy density ratio $\eta/s$. It develops a one-loop gravitational path-integral framework that includes Schwarzian modes and nontrivial coupling to zero modes, without reducing to a two-dimensional JT theory, to compute corrections to boundary correlators. The main finding is that while tree-level holography preserves $\eta/s = 1/(4\pi)$, a low-temperature one-loop coupling between shear fluctuations and a Schwarzian mode drives $\eta/s$ below the bound, with an entropy correction $S_{one\-loop} \sim \tfrac{3}{2}\log(T/T_q)$ and a characteristic scale $T_q$. This work highlights a concrete mechanism by which quantum throat dynamics can modify universal holographic transport and motivates deeper exploration of Schwarzian dynamics in higher-dimensional AdS/CFT.

Abstract

Near-extremal black holes are known to contain strong quantum fluctuations in their near-horizon near-AdS$_2$ throat region governed by an effective action that includes Schwarzian modes. These fluctuations lead to one-loop corrections in the gravitational path integral that are essential in understanding the thermodynamics of near-extremal black holes at low temperatures where they become more dominant that the semi-classical answer. We explore the implications of these quantum fluctuations for near-extremal asymptotically AdS$_4$ black branes in the context of the AdS/CFT correspondence. We note that at one-loop level there is a coupling of the shear gravitational fluctuations to one of the would-be zero modes. This coupling affects the retarded Green's function in a way that leads to a low temperature violation of the shear viscosity to entropy density bound.

One-loop Corrected Holographic Shear Viscosity to Entropy Density Ratio at Low Temperatures

TL;DR

The paper addresses how quantum fluctuations in the near-horizon throat of near-extremal black branes affect holographic transport, focusing on the shear viscosity to entropy density ratio . It develops a one-loop gravitational path-integral framework that includes Schwarzian modes and nontrivial coupling to zero modes, without reducing to a two-dimensional JT theory, to compute corrections to boundary correlators. The main finding is that while tree-level holography preserves , a low-temperature one-loop coupling between shear fluctuations and a Schwarzian mode drives below the bound, with an entropy correction and a characteristic scale . This work highlights a concrete mechanism by which quantum throat dynamics can modify universal holographic transport and motivates deeper exploration of Schwarzian dynamics in higher-dimensional AdS/CFT.

Abstract

Near-extremal black holes are known to contain strong quantum fluctuations in their near-horizon near-AdS throat region governed by an effective action that includes Schwarzian modes. These fluctuations lead to one-loop corrections in the gravitational path integral that are essential in understanding the thermodynamics of near-extremal black holes at low temperatures where they become more dominant that the semi-classical answer. We explore the implications of these quantum fluctuations for near-extremal asymptotically AdS black branes in the context of the AdS/CFT correspondence. We note that at one-loop level there is a coupling of the shear gravitational fluctuations to one of the would-be zero modes. This coupling affects the retarded Green's function in a way that leads to a low temperature violation of the shear viscosity to entropy density bound.
Paper Structure (14 sections, 70 equations, 2 figures)

This paper contains 14 sections, 70 equations, 2 figures.

Table of Contents

  1. Introduction
  2. One-loop correction to the Euclidean path integral: a brief review
  3. Review of the Reissner-Nordström corrected thermodynamics below $T_q$
  4. AdS/CFT correlation function: from tree level to one-loop formalism
  5. One-loop corrected correlation functions
  6. Shear viscosity: non-zero temperature and one-loop correction
  7. Small temperature expansion on tree level
  8. Inner region:
  9. Outer region:
  10. Match solutions in the two regions
  11. One-loop contribution
  12. Conclusions
  13. The structure of the Lichnerowicz operator
  14. Integral back to Lorentz

Figures (2)

  • Figure 1: The one-loop quantum-corrected shear viscosity to entropy density ratio, $\eta/s$. Parameters are set by $r_0=1,L=2,\kappa_4=1,V=1$.
  • Figure 2: The one-loop quantum-corrected shear viscosity to entropy density ratio, $\eta/s$ is shown by the orange surface, depending on $\{T,\mu\}$. The blue surface is $\tfrac{1}{4\pi}$ for reference. Parameters are set by $L=2,\kappa_4=1,V=1$. In this plot, $\mu$ starts from 0.1. $\eta/s$ recovers $\tfrac{1}{4\pi}$ for large $T$ or large $\mu$.