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arXiv · 2112.06942

The fate of Parisi-Sourlas supersymmetry in Random Field models

Apratim Kaviraj·Slava Rychkov·Emilio Trevisani
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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.

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Apratim Kaviraj, Slava Rychkov, Emilio Trevisani. 2021-12-13. The fate of Parisi-Sourlas supersymmetry in Random Field models. https://doi.org/10.1103/physrevlett.129.045701

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