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

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 $2\le d\le 4$ 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 the absence of supersymmetry.

Figure 1

Comparison between the ratios $r_G(d)$ and $r_{\mathrm{free}}(d)$. The continuous line represents $r_G(d)$, while the dashed line corresponds to $r_{\mathrm{free}}(d)$. The point represents the ratio $k^{\prime }/k$ for the $O(n)$ nonlinear $\sigma$ model at large $n$ and $d=3$ [see Eq. (23)].