Universal properties of the U(1) current at deconfined quantum critical points: comparison with predictions from gauge/gravity duality

TL;DR

This paper compares the universal properties of the U(1) current at deconfined quantum critical points in 2+1 dimensions with predictions from gauge/gravity duality, revealing remarkable agreement and potential for testing duality in condensed matter systems.

Contribution

It derives an exact formula for the U(1) current's central charge at quantum criticality and compares it with gauge-gravity duality predictions, highlighting similarities in 2+1 dimensions.

Findings

Exact formula for the U(1) current's central charge at criticality.

Strong agreement between condensed matter results and gauge/gravity duality in 2+1D.

Finite temperature charge susceptibility matches duality predictions.

Abstract

The deconfined quantum critical point of a two-dimensional SU(N) antiferromagnet is governed by an Abelian Higgs model in $d=2+1$ spacetime dimensions featuring $N$ complex scalar fields. In this context, we derive for $2\leq d\leq 4$ an exact formula for the central charge of the U(1) current in terms of the gauge coupling at quantum criticality and compare it with the corresponding result obtained using gauge-gravity duality. There is a remarkable similarity precisely for $d=2+1$. In this case the amplitude of the current correlation function has the same form as predicted by the gauge-gravity duality. We also compare finite temperature results for the charge susceptibility in the large $N$ limit with the result predicted by the gauge-gravity duality. Our results suggest that condensed matter systems at quantum criticality may provide interesting quantitative tests of the gauge-gravity duality even in absence of supersymmetry.