Quantum phase transitions beyond the Landau-Ginzburg paradigm and supersymmetry

TL;DR

This paper explores how supersymmetric U(1) gauge theories in 2+1 dimensions serve as rigorous examples of quantum phase transitions beyond the traditional Landau-Ginzburg paradigm, linking condensed matter and particle theory insights.

Contribution

It establishes a connection between supersymmetric gauge theories and deconfined quantum critical points in condensed matter physics, providing rigorous examples beyond the Landau-Ginzburg-Wilson framework.

Findings

Supersymmetric U(1) gauge theories model non-Landau-Ginzburg quantum phase transitions.

Connections between supersymmetric mirror symmetry and condensed matter dualities.

Examples of deconfined criticality in supersymmetric theories.

Abstract

We make connections between studies in the condensed matter literature on quantum phase transitions in square lattice antiferromagnets, and results in the particle theory literature on abelian supersymmetric gauge theories in 2+1 dimensions. In particular, we point out that supersymmetric U(1) gauge theories (with particle content similar, but not identical, to those of theories of doped antiferromagnets) provide rigorous examples of quantum phase transitions which do not obey the Landau-Ginzburg-Wilson paradigm (often referred to as transitions realizing "deconfined criticality"). We also make connections between supersymmetric mirror symmetries and condensed matter particle-vortex dualities.