Towards strange metallic holography

Abstract

Abstract:We initiate a holographic model building approach to 'strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent z appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group flow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when z ≥ 2. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.

Transport properties of spacetime-filling branes

“…In the limit T b L 2 → 0, the adjoint and fundamental terms in (1.1) decouple, and the probe approximation of [19] is recovered. However, in [20] it was argued that in certain cases, for non trivial values of the U(1) field in (1.3), this approximation is not valid: the backreaction of the fundamental matter is generically important in the IR description of the theory. This was confirmed in the specific case of the intersection of a stack of D3-branes with smeared D7-branes at finite charge density [21], where a perturbative solution in T b L 2 was constructed and shown to break down in the interior of the bulk geometry.…”

Analytic Lifshitz black holes in higher dimensions

“…The difficulty of embedding Lifshitz black holes in string theory was also investigated in Refs. [12,13,14]. The holographic description of asymptotically Lifshitz spacetimes was studied in [15].…”

Holographic quenches and fermionic spectral functions

“…We deliberately choose parameters such that 2ν k F > 1, so that sharp quasiparticles are formed in the finite density system. It is however by now well understood that, when backreaction from bulk fermions is taken into account, the RN black hole is quantum mechanically unstable to the formation of an electron star [29][30][31][32][33] (see [34] for a review). This also corresponds to a thermodynamic instability, in the sense that for fixed temperature and chemical potential, the electron star solution has lower free energy than the RN black brane.…”