Emergence of supersymmetric quantum electrodynamics

TL;DR

This paper demonstrates the emergence of supersymmetric quantum electrodynamics (SQED) at a quantum phase transition on the surface of a topological insulator, providing a novel link between condensed matter physics and supersymmetric gauge theories.

Contribution

It presents the first example of emergent supersymmetric gauge theory in a condensed matter system, specifically showing SQED arising at a tricritical point on a topological insulator surface.

Findings

Emergent supersymmetric gauge theory at a surface phase transition.

Exact critical exponents and optical conductivity predictions.

Identification of the supersymmetric XYZ model as the effective theory.

Abstract

Supersymmetric (SUSY) gauge theories such as the Minimal Supersymmetric Standard Model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator (TI) hosting three Dirac cones, such as the topological Kondo insulator SmB$_6$. At the quantum tricritical point between the surface Dirac semimetal and nematic PDW phases, three massless bosonic Cooper pair fields emerge as the superpartners of three massless surface Dirac fermions. The resulting low-energy effective theory is the supersymmetric XYZ model, which is dual by mirror symmetry to $\mathcal{N}=2$ supersymmetric quantum electrodynamics (SQED) in 2+1 dimensions, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine exactly certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point, which may be measured in future experiments.