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 hosting three Dirac cones, such as the topological Kondo insulator SmB6. 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 N=2 supersymmetric quantum electrodynamics in 2+1 dimensions, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point exactly, which may be measured in future experiments.
Bibliographical noteFunding Information:
We would like to thank K. Sun, G. Torroba, and W. Witczak-Krempa for helpful discussions. This work was supported in part by the NSFC under Grant No.11474175 at Tsinghua University (S.K.J. and H.Y.), and by NSERC Grant No.RGPIN-2014-4608, the CRC Program, CIFAR, and the University of Alberta (C.H.L. and J.M.). J.M. is grateful for the hospitality of the Institute for Advanced Study, Tsinghua University where this work was initiated.