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Updated: Sep 2, 2025

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Parisi-Sourlas Supersymmetry in Random Field Models
Apratim Kaviraj1,2,3, Slava Rychkov2,4, Emilio Trevisani2,5
1Institut de Physique Théorique Philippe Meyer, ENS, Université PSL, CNRS Sorbonne Université, Université de Paris, F-75005 Paris, France.
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 ϕ^{3} model but not for the RF ϕ^{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 a 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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