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The fate of Parisi-Sourlas supersymmetry in Random Field models

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arxiv 2112.06942 v3 pith:KATGVPCH submitted 2021-12-13 cond-mat.stat-mech hep-th

Apratim Kaviraj , Slava Rychkov , Emilio Trevisani This is my paper · ORCID
classification cond-mat.stat-mechhep-th
keywords fieldsusyinteractionsmodelnumericalparisi-sourlaspointrandom
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ising surface defects can get dirty

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Replica one-loop RG of Wilson-Fisher theory with surface random field yields a mixed-stable dirty defect fixed point and logarithmic multiplets in the N o0 limit.

  2. Parisi-Sourlas Supertranslation and Scale without Conformal symmetry

    hep-th 2024-11 accept novelty 7.0 of 10

    Supertranslation symmetry protects the virial current's scaling dimension, giving eight perturbative scale-invariant but non-conformal fixed points in a quartic superfield model.

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