Quantum Criticality and Yang-Mills Gauge Theory

TL;DR

The paper constructs nonrelativistic Yang-Mills gauge theories in $D{+}1$ dimensions with $z=2$ Lifshitz scaling, linking their free-field ground state to the partition function of $D$-dimensional relativistic YM through a detailed-balance structure. At the Gaussian fixed point, the theory exhibits a ground-state wavefunction tied to $D$-dimensional YM and displays a $D{-}1$ gauge-polarization spectrum with a $\omega^2=(\mathbf{k}^2)^2/\lambda^2$ dispersion; the theory is asymptotically free in $4{+}1$ dimensions. A relevant deformation can drive the IR to a relativistic $z=1$ theory, with a tunable effective YM coupling and modified dispersion, while large-$N$ considerations hint at gravity duals. The work opens avenues for supersymmetric and string-theoretic realizations and potential holographic descriptions of nonrelativistic RG fixed points in higher 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.