Large-density field theory, viscosity, and "$2k_F$" singularities from string duals

TL;DR

The paper shows that large charge density can provide a controlled string-dual description of a field theory without requiring large N_c, using the NS5/F1 system in AdS_3 × T^4 × S^3 as a finite-density 5+1D setup. Through exact worldsheet CFT methods, Polchinski and Silverstein demonstrate that α' corrections do not alter the perpendicular-to-string shear viscosity (η/s = 1/(4π)) but cause the parallel flow to approach a vanishing η/s ∝ T^2 at low T, revealing highly anisotropic hydrodynamics. The analysis also uncovers low-frequency, finite-momentum singularities in correlation functions, interpreted as a strong-coupling analogue of 2k_F singularities with long-string configurations acting as the relevant composite operators, and a Luttinger-like relation between density and momentum-space singular surfaces. These results provide a clean, calculable example where a string-theoretic UV completion plays a central role in finite-density holography and may illuminate strongly coupled condensed matter analogues. The work highlights the interplay between density, geometry, and stringy corrections in shaping transport and spectral properties at strong coupling.

Abstract

We analyze systems where an effective large-N expansion arises naturally in gauge theories without a large number of colors: a sufficiently large charge density alone can produce a perturbative string ('tHooft) expansion. One example is simply the well-known NS5/F1 system dual to $AdS_3\times T^4\times S^3$, here viewed as a 5+1 dimensional theory at finite density. This model is completely stable, and we find that the existing string-theoretic solution of this model yields two interesting results. First, it indicates that the shear viscosity is not corrected by $α'$ effects in this system. For flow perpendicular to the F1 strings the viscosity to entropy ratio take the usual value $1/4π$, but for flow parallel to the F1's it vanishes as $T^2$ at low temperature. Secondly, it encodes singularities in correlation functions coming from low-frequency modes at a finite value of the momentum along the $T^4$ directions. This may provide a strong coupling analogue of finite density condensed matter systems for which fermionic constituents of larger operators contribute so-called "$2k_F$" singularities. In the NS5/F1 example, stretched strings on the gravity side play the role of these composite operators. We explore the analogue for our system of the Luttinger relation between charge density and the volume bounded by these singular surfaces. This model provides a clean example where the string-theoretic UV completion of the gravity dual to a finite density field theory plays a significant and calculable role.