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Résumé |
I will discuss some recent results on random field (RF) models and their
connections to Parisi–Sourlas (PS) supersymmetry (SUSY), dimensional reduction,
and dimensional uplift. The first part will focus on an RG framework that we
developed to explain the emergence of PS SUSY at the critical point of the RF
Ising model in d=5, as well as its absence in lower dimensions. This will be
followed by a new proof of PS dimensional reduction, which relates PS SUSY
theories in d dimensions to theories in d-2 dimensions, together with the inverse
construction of dimensional uplift, which associates to a given conformal field
theory (CFT) a higher-dimensional CFT with PS SUSY. The talk will conclude with a
brief discussion of how these connections extend to the presence of extended
operators (defects). |
