Emergent Space-time Supersymmetry at the Boundary of a Topological Phase

TL;DR

This paper demonstrates that supersymmetry naturally emerges at the boundary of topological superconductors during quantum phase transitions, revealing deep links between topological phases and supersymmetry with potential experimental implications.

Contribution

It shows that supersymmetry appears at the boundary of topological superconductors during phase transitions, providing a new theoretical connection between topological matter and SUSY.

Findings

Supersymmetry emerges at the boundary of topological superconductors during quantum phase transitions.

Exact relations and universal critical exponents can be derived from supersymmetry.

Potential experimental signatures include relations between different measurement quantities.

Abstract

In contrast to ordinary symmetries, supersymmetry interchanges bosons and fermions. Originally proposed as a symmetry of our universe, it still awaits experimental verification. Here we theoretically show that supersymmetry emerges naturally in topological superconductors, which are well-known condensed matter systems. Specifically, we argue that the quantum phase transitions at the boundary of topological superconductors in both two and three dimensions display supersymmetry when probed at long distances and times. Supersymmetry entails several experimental consequences for these systems, such as, exact relations between quantities measured in disparate experiments, and in some cases, exact knowledge of the universal critical exponents. The topological surface states themselves may be interpreted as arising from spontaneously broken supersymmetry, indicating a deep relation between topological phases and SUSY. We discuss prospects for experimental realization in films of superfluid He$_3$-B.