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Register a new userConductivities for Hyperscaling Violating Geometries
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Authors
Andreas Karch
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We show that many results about holographic conductivities in geometries with hyperscaling violating scaling can be reproduced from simple scaling laws in the dual field theory. We show that the electro-magnetic response of probe branes in these systems require at least one additional scaling parameter Phi beyond the usual dynamical exponent z and hyperscaling violating exponent theta, as also pointed out in earlier work. We show that the scaling exponents can be chosen in such a way that the temperature dependence of DC conductivity and Hall angle in strange metals can be reproduced.
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We analytically compute the thermoelectric conductivities at zero frequency (DC) in the holographic dual of a four dimensional Einstein-Maxwell-Axion-Dilaton theory that admits a class of asymptotically hyperscaling violating Lifshitz backgrounds with a dynamical exponent $z$ and hyperscaling violating parameter $theta$. We show that the heat current in the dual Lifshitz theory involves the energy flux, which is an irrelevant operator for $z>1$. The linearized fluctuations relevant for computing the thermoelectric conductivities turn on a source for this irrelevant operator, leading to several novel and non-trivial aspects in the holographic renormalization procedure and the identification of the physical observables in the dual theory. Moreover, imposing Dirichlet or Neumann boundary conditions on the spatial components of one of the two Maxwell fields present leads to different thermoelectric conductivities. Dirichlet boundary conditions reproduce the thermoelectric DC conductivities obtained from the near horizon analysis of Donos and Gauntlett, while Neumann boundary conditions result in a new set of DC conductivities. We make preliminary analytical estimates for the temperature behavior of the thermoelectric matrix in appropriate regions of parameter space. In particular, at large temperatures we find that the only case which could lead to a linear resistivity $rho sim T$ corresponds to $z=4/3$.
We explore in greater detail our investigations of shear diffusion in hyperscaling violating Lifshitz theories in arXiv:1604.05092 [hep-th]. This adapts and generalizes the membrane-paradigm-like analysis of Kovtun, Son and Starinets for shear gravitational perturbations in the near horizon region given certain self-consistent approximations, leading to the shear diffusion constant on an appropriately defined stretched horizon. In theories containing a gauge field, some of the metric perturbations mix with some of the gauge field perturbations and the above analysis is somewhat more complicated. We find a similar near-horizon analysis can be obtained in terms of new field variables involving a linear combination of the metric and the gauge field perturbation resulting in a corresponding diffusion equation. Thereby as before, for theories with Lifshitz and hyperscaling violating exponents $z, theta$ satisfying $z<4-theta$ in four bulk dimensions, our analysis here results in a similar expression for the shear diffusion constant with power-law scaling with temperature suggesting universal behaviour in relation to the viscosity bound. For $z=4-theta$, we find logarithmic behaviour.
We construct numerically finite density domain-wall solutions which interpolate between two $AdS_4$ fixed points and exhibit an intermediate regime of hyperscaling violation, with or without Lifshitz scaling. Such RG flows can be realized in gravitational models containing a dilatonic scalar and a massive vector field with appropriate choices of the scalar potential and couplings. The infrared $AdS_4$ fixed point describes a new ground state for strongly coupled quantum systems realizing such scalings, thus avoiding the well-known extensive zero temperature entropy associated with $AdS_2 times mathbb{R}^2$. We also examine the zero temperature behavior of the optical conductivity in these backgrounds and identify two scaling regimes before the UV CFT scaling is reached. The scaling of the conductivity is controlled by the emergent IR conformal symmetry at very low frequencies, and by the intermediate scaling regime at higher frequencies.
By employing the holographic operator mixing technique to deal with coupled perturbations in the gauge/gravity duality, I numerically compute the real and imaginary parts of the diagonal and Hall AC conductivities in a strongly coupled quantum field theory dual to a bulk condensate of magnetic monopoles. The results obtained show that a conclusion previously derived in the literature, namely, the vanishing of holographic DC conductivities in 3-dimensional strongly coupled quantum field theories dual to a 4-dimensional bulk magnetic monopole condensate, also applies to the calculation of diagonal and Hall conductivities in the presence of a topological $theta$-term. Therefore, the condensation of magnetic monopoles in the bulk is suggested as a rather general and robust mechanism to generate dual strongly coupled quantum field theories with zero DC conductivities. The interplay between frequency, $theta$-angle and the characteristic mass scale of the monopole condensate on the results for the conductivities is also investigated.
We find exact, analytic solutions of the holographic AC conductivity at arbitrary frequency $omega$ and temperature $T$, in contrast to previous works where the AC conductivity was analytically obtained usually at small $omega$ and $T$. These solutions enable us to study the analyticity properties of the current-current correlator $G(omega)$ in detail. The first system we study is the AdS$_5$ planar black hole with momentum dissipation, whose extremal limit has an AdS$_2$ factor. Then we study an AdS$_4$ Einstein-dilaton system whose special cases are maximal gauged supergravities. The solutions show how the poles move and how branch cuts emerge as the temperature varies. As a byproduct, we obtain an $R$-current correlator in $mathcal{N}=4$ super-Yang-Mills theory on a sphere at finite temperature in the large $N$ and strong coupling limit.
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