Quantum Criticality and Yang-Mills Gauge Theory

TL;DR

This paper introduces nonrelativistic Yang-Mills gauge theories with quantum critical behavior, relating their ground states to relativistic Yang-Mills theories and exploring their scaling, deformations, and potential gravity duals.

Contribution

It presents a new class of nonrelativistic Yang-Mills theories with quantum criticality, logarithmic scaling, and connections to gravity duals, expanding understanding of gauge theories in nonrelativistic regimes.

Findings

Exhibits quantum critical behavior with gapless excitations and z=2.

Ground state wavefunction related to relativistic Yang-Mills partition function.

Gauge couplings show asymptotic freedom in 4+1 dimensions.

Abstract

We present a family of nonrelativistic Yang-Mills gauge theories in D+1 dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2. The ground state wavefunction is intimately related to the partition function of relativistic Yang-Mills in D dimensions. The gauge couplings exhibit logarithmic scaling and asymptotic freedom in the upper critical spacetime dimension, equal to 4+1. The theories can be deformed in the infrared by a relevant operator that restores Poincare invariance as an accidental symmetry. In the large-N limit, our nonrelativistic gauge theories can be expected to have weakly curved gravity duals.