Hyperscaling-Violation on Probe D-Branes

TL;DR

This work identifies zero-temperature quantum critical points in the D3/D7 and D3/D5 holographic systems at finite density, showing they are governed by a non-relativistic, scale-invariant theory with hyperscaling violation. The authors establish the exponents $z=2$ and $\theta=1$ from both the low-energy sound modes and thermodynamics, with the non-relativistic energy related to the pressure as $e=p$ for D3/D7 and $e=p/2$ for D3/D5. They compute the finite-density thermodynamics exactly, determine normal and zero-sound dispersion relations that corroborate the scaling, and extend to small finite temperature to extract the exponents $α$ and $ν$ via $zν=1$, finding $α=0$, $ν=1/2$ for D3/D7 and $α=1/2$, $ν=1/2$ for D3/D5. The results demonstrate hyperscaling violation at a quantum critical point and provide detailed, testable predictions for the behavior of thermodynamics and collective modes in these strongly coupled, probe-brane systems. The findings offer insight into non-relativistic fixed points and potential connections to entanglement structure and hidden Fermi surfaces in holographic matter.

Abstract

For the field theories dual to D3/D7- and D3/D5-brane systems we find non-relativistic finite density fixed points exhibiting a violation of hyperscaling. This violation is measured by the critical exponent $θ=1$ while the dynamical critical exponent is $z=2$. At zero temperature we compute the thermodynamic potentials, the speed of normal sound, and the speed of zero sound for both these massive D3/D(2n+1)-brane systems near their non-relativistic fixed points. Moreover, we determine the first correction to the free energy for small temperatures yielding the critical exponents $α$ and $ν$.

Figures (1)

• Figure 1: Coordinate directions in which the Dp--branes extend are marked by x. While D3- and D7-branes share the four Minkowski directions, D3-- and D5--branes share only a $2+1$-dimensional plane in the four Minkowski directions.