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Notes on Properties of Holographic Matter

Andreas Karch, Manuela Kulaxizi, Andrei Parnachev

TL;DR

This work analyzes holographic matter from finite-density Dp/Dq probe-brane systems and identifies two universal low-temperature quantities—specific heat and DC conductivity—that are independent of the probe dimension q and controlled by the dynamics of a single heavy quark string, via the DBI action and drag-force arguments. The authors derive explicit expressions for the free energy shifts Δm of a heavy quark, show the resulting heat capacity scales as c_V ∝ T^{2/(5−p)} and, in turn, the DC conductivity scales as σ ∝ d λ^{−1/(5−p)} T^{−(7−p)/(5−p)} in the density-dominated regime, with mass and embedding details becoming irrelevant at low T. They also treat massive embeddings, demonstrate the universality persists with a string-spike picture, and discuss zero-density resistivity ρ_0 which depends on defect dimension ds; examples include ρ_0 ∼ T^{−2} for p=4, q=8, ds=3, and conditions yielding linear-in-T resistivity in certain cases. Collectively, the results provide a unified, q-independent view of thermodynamics and transport in holographic matter and offer insights into potential non-Fermi-liquid behavior and strange-metal phenomenology in defect field theories. $c_V o ext{leading} imes T^{2/(5-p)}$, $σ o d \, λ^{-1/(5-p)} \, T^{-(7-p)/(5-p)}$ in the density-dominated regime.

Abstract

Probe branes with finite worldvolume electric flux in the background created by a stack of Dp branes describe holographically strongly interacting fundamental matter at finite density. We identify two quantities whose leading low temperature behavior is independent of the dimensionality of the probe branes: specific heat and DC conductivity. This behavior can be inferred from the dynamics of the fundamental strings which provide a good description of the probe branes in the regime of low temperatures and finite densities. We also comment on the speed of sound on the branes and the temperature dependence of DC conductivity at vanishing charge density.

Notes on Properties of Holographic Matter

TL;DR

This work analyzes holographic matter from finite-density Dp/Dq probe-brane systems and identifies two universal low-temperature quantities—specific heat and DC conductivity—that are independent of the probe dimension q and controlled by the dynamics of a single heavy quark string, via the DBI action and drag-force arguments. The authors derive explicit expressions for the free energy shifts Δm of a heavy quark, show the resulting heat capacity scales as c_V ∝ T^{2/(5−p)} and, in turn, the DC conductivity scales as σ ∝ d λ^{−1/(5−p)} T^{−(7−p)/(5−p)} in the density-dominated regime, with mass and embedding details becoming irrelevant at low T. They also treat massive embeddings, demonstrate the universality persists with a string-spike picture, and discuss zero-density resistivity ρ_0 which depends on defect dimension ds; examples include ρ_0 ∼ T^{−2} for p=4, q=8, ds=3, and conditions yielding linear-in-T resistivity in certain cases. Collectively, the results provide a unified, q-independent view of thermodynamics and transport in holographic matter and offer insights into potential non-Fermi-liquid behavior and strange-metal phenomenology in defect field theories. , in the density-dominated regime.

Abstract

Probe branes with finite worldvolume electric flux in the background created by a stack of Dp branes describe holographically strongly interacting fundamental matter at finite density. We identify two quantities whose leading low temperature behavior is independent of the dimensionality of the probe branes: specific heat and DC conductivity. This behavior can be inferred from the dynamics of the fundamental strings which provide a good description of the probe branes in the regime of low temperatures and finite densities. We also comment on the speed of sound on the branes and the temperature dependence of DC conductivity at vanishing charge density.

Paper Structure

This paper contains 7 sections, 40 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction and Results
  2. Thermodynamics of the Dp brane
  3. Free energy of a single quark and the Heat Capacity of a Dq probe
  4. Massive quarks and specific heat
  5. Drag on a single quark and DC conductivity of the Dq probe
  6. Resistivity at zero density
  7. Conclusions

Figures (2)

  • Figure 1: Speed of sound squared $c^2$, for all Dp/Dq systems with p=2, 3 or 4 and 4 or 6 ND directions, as a function of $d_s$, the number of spatial dimensions. Shape/color distinguishes p=4 (red circles), p=3 (green squares) and p=2 (blue triangles). Open/filled symbols are 6/4 ND direction configurations. For p=3 the open and filled squares lie on top of each other.
  • Figure 2: Resistivity scaling factor $x$, for all Dp/Dq systems with p=2, 3 or 4 and 4 or 6 ND directions, as a function of $d_s$, the number of spatial dimensions. Shape/color distinguishes p=4 (red circles), p=3 (green squares) and p=2 (blue triangles). Open/filled symbols are 6/4 ND direction configurations.