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<p>The strongly-coupled 3-dimensional theory, holographically dual to black branes at fixed chemical potential <i>μ</i> and temperature <i>T</i> ≪ <i>μ</i> is considered in AdS<sub>4</sub> Einstein-Maxwell theory. The retarded Green’s functions at frequency <i>ω</i> is calculated using holography in the regime <i>ω</i>, <i>T</i> ≪ <i>μ</i> but otherwise arbitrary. When the transverse space has finite volume, there is a non-zero energy scale <i>E</i><sub>gap</sub>, scaling as 1/<i>μ</i> for large <i>μ</i>, below which quantum-gravitational corrections due to the fluctuations of the nearly-gapless Schwarzian modes become important. Such corrections to the retarded Green’s function are calculated at different relative values of <i>ω</i>, <i>T</i>, and <i>E</i><sub>gap</sub>. The <i>ω</i> → 0 limit is used to define the shear viscosity <i>η</i>. As the temperature is lowered below <i>μ</i>, quantum corrections are found to increase the value of <i>η</i> with respect to its semiclassical value. The quantum-corrected result for <i>η</i> diverges as <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msqrt> <mrow> <msub> <mi mathvariant="normal">E</mi> <mi>gap</mi> </msub> <mo>/</mo> <mi>T</mi> </mrow> </msqrt> </math></EquationSource> <EquationSource Format="TEX">\( \sqrt{{\mathrm{E}}_{\mathrm{gap}}/T} \)</EquationSource> </InlineEquation> at <i>T</i> ≪ <i>E</i><sub>gap</sub>, in accord with corresponding results for the absorption cross section. The quantum result for the ratio <i>η</i>/<i>s</i>, where <i>s</i> is the entropy density, dips below the semiclassical limit of 1/4<i>π</i> when <i>E</i><sub>gap</sub> ≪ <i>T</i> ≪ <i>μ</i>, then turns back to increase towards lower temperatures, and finally diverges at temperatures much below <i>E</i><sub>gap</sub>.</p>

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Holographic shear correlators at low temperatures, and quantum η/s

  • 期刊论文

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  • 发表日期：

    2026年7月16日

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  • Alexandros Kanargias,
  • Elias Kiritsis,
  • Sameer Murthy,
  • Olga Papadoulaki,
  • Achilleas P. Porfyriadis

摘要

The strongly-coupled 3-dimensional theory, holographically dual to black branes at fixed chemical potential μ and temperature T ≪ μ is considered in AdS4 Einstein-Maxwell theory. The retarded Green’s functions at frequency ω is calculated using holography in the regime ω, T ≪ μ but otherwise arbitrary. When the transverse space has finite volume, there is a non-zero energy scale Egap, scaling as 1/μ for large μ, below which quantum-gravitational corrections due to the fluctuations of the nearly-gapless Schwarzian modes become important. Such corrections to the retarded Green’s function are calculated at different relative values of ω, T, and Egap. The ω → 0 limit is used to define the shear viscosity η. As the temperature is lowered below μ, quantum corrections are found to increase the value of η with respect to its semiclassical value. The quantum-corrected result for η diverges as E gap / T \( \sqrt{{\mathrm{E}}_{\mathrm{gap}}/T} \) at T ≪ Egap, in accord with corresponding results for the absorption cross section. The quantum result for the ratio η/s, where s is the entropy density, dips below the semiclassical limit of 1/4π when Egap ≪ T ≪ μ, then turns back to increase towards lower temperatures, and finally diverges at temperatures much below Egap.