  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.
