Hyperscaling-Violation on Probe D-Branes

TL;DR

This paper investigates non-relativistic fixed points with hyperscaling violation in D3/D7 and D3/D5-brane systems, analyzing thermodynamics and critical exponents near these points.

Contribution

It provides the first detailed analysis of hyperscaling violation and critical exponents in D-brane systems at non-relativistic fixed points.

Findings

Hyperscaling violation measured by $ heta=1$ with $z=2$.

Computed thermodynamic potentials, sound speeds, and free energy corrections.

Determined critical exponents $eta$, $ u$ near fixed points.

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 $\theta=1$ 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 $\alpha$ and $\nu$.