Parisi-Sourlas Supersymmetry in Random Field Models
Apratim Kaviraj, Slava Rychkov, Emilio Trevisani
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.
Topics & Concepts
SupersymmetryPhysicsQuartic functionField (mathematics)Renormalization groupTheoretical physicsConformal field theoryMathematical physicsConjectureConformal mapFixed pointQuantum electrodynamicsMathematicsCombinatoricsPure mathematicsMathematical analysisTheoretical and Computational PhysicsBlack Holes and Theoretical PhysicsGeometry and complex manifolds