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arXiv:0902.0364 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

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

Flavio S. Nogueira

Published May 8, 2009• 1 citation
arXivHTMLPDF

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 $2\ensuremath{\le}d\ensuremath{\le}4$ 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.

DOI
10.1103/physrevd.79.105007

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The deconfined quantum critical point of a two-dimensional SU(N)SU(N)SU(N) antiferromagnet is governed by an Abelian Higgs model in d=2+1d=2+1d=2+1 spacetime dimensions featuring NNN complex scalar fields. In this context, we derive for 2\ensuremath≤d\ensuremath≤42\ensuremath{\le}d\ensuremath{\le}42\ensuremath≤d\ensuremath≤4 an exact formula for the central charge of the U(1)U(1)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+1d=2+1d=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 NNN 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.
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The deconfined phase of (2+12+12+1)-dimensional Zk{\mathbb{Z}}_{k}Zk​ gauge theory exhibits topological order, with eee and mmm anyons that have a $2\ensuremath{\pi}/k$ braiding phase. Proliferating either eee or mmm drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges eee and mmm anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theory with a mutual Chern-Simons term at level kkk to describe the vicinity of the multicritical point for $k\ensuremath{\ge}4$. The emergence of a global $\mathrm{U}{(1)}^{\mathrm{top}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}^{\mathrm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved U(1) current with protected scaling dimension; (2) the first-order line emanating from the critical point for k=2k=2k=2 disappears generically for sufficiently large kkk; (3) the correlation length exponent approaches that of the three-dimensional XY model with corrections of order 1/k21/{k}^{2}1/k2 in the large-kkk limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.