  Topological states of electrons present new avenues to explore the rich
phenomenology of correlated quantum matter. Topological insulators (TIs) in
particular offer an experimental setting to study novel quantum critical points
(QCPs) of massless Dirac fermions, which exist on the sample's surface. Here,
we obtain exact results for the zero- and finite-temperature optical
conductivity at the semimetal-superconductor QCP for these topological surface
states. This strongly interacting QCP is described by a scale invariant theory
with emergent supersymmetry, which is a unique symmetry mixing bosons and
fermions. We show that supersymmetry implies exact relations between the
optical conductivity and two otherwise unrelated properties: the shear
viscosity and the entanglement entropy. We discuss experimental considerations
for the observation of these signatures in TIs.
