Speaker
Description
Parisi-Sourlas (PS) supersymmetry is known to emerge in some models with random field type of disorder. When PS SUSY is present, the $d$-dimensional theory allows for a $d−2$-dimensional description. In this talk I focus on the reversed question and provide new indications that any given CFT$_{d−2}$ can be uplifted to a PS SUSY CFT$_d$. I show that any scalar four-point function of a CFT$_{d−2}$ is mapped to a set of 43 four-point functions of the uplifted CFT$_d$ which are related to each other by SUSY and satisfy all necessary bootstrap axioms. As a byproduct this will imply 43 non trivial relations between conformal blocks across dimensions. I then explain why all diagonal minimal models admit an uplift and show exact results for correlators and CFT data of the 4d uplift of the Ising model. Despite being strongly coupled 4d CFTs, the uplifted minimal models contain infinitely many conserved currents and are expected to be integrable. Finally I will mention how to generalize the uplift in the presence of conformal defects like boundaries and Wilson lines.
