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Hyperscaling-Violation on Probe D-Branes

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 $ν$.