The fate of Parisi-Sourlas supersymmetry in Random Field models

TL;DR

This paper investigates the fate of Parisi-Sourlas supersymmetry in random field models, showing that SUSY is broken by relevant interactions in certain dimensions, aligning with numerical findings.

Contribution

It demonstrates that the SUSY fixed point is not reached due to new relevant SUSY-breaking interactions, using a systematic perturbative RG approach.

Findings

SUSY fixed point is not reached in RF models with certain potentials.

Perturbative RG analysis confirms numerical results.

Relevant SUSY-breaking interactions prevent SUSY from emerging.

Abstract

By the Parisi-Sourlas conjecture, the critical point of a theory with random field (RF) disorder is described by a supersymmeric (SUSY) conformal field theory (CFT), related to a $d-2$ dimensional CFT without SUSY. Numerical studies indicate that this is true for the RF $\phi^3$ model but not for RF $\phi^4$ model in $d<5$ dimensions. Here we argue that the SUSY fixed point is not reached because of new relevant SUSY-breaking interactions. We use perturbative renormalization group in a judiciously chosen field basis, allowing systematic exploration of the space of interactions. Our computations agree with the numerical results for both cubic and quartic potential.