Is there supersymmetric Lee-Yang fixed point in three dimensions?

TL;DR

This paper investigates the existence of a supersymmetric Lee-Yang fixed point in three dimensions using conformal bootstrap methods, concluding it likely does not exist and suggesting any related phase transition would be first order.

Contribution

The study applies truncated conformal bootstrap to explore higher-dimensional analogues of the supersymmetric Lee-Yang fixed point, providing evidence for its absence in three dimensions.

Findings

Candidate fixed points vanish below three dimensions

No supersymmetric Lee-Yang fixed point in three dimensions

Possible first order phase transition if related phenomena occur

Abstract

The supersymmetric Lee-Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit non-unitary. A natural question is if there is an analogue of supersymmetric Lee-Yang fixed point in higher dimensions. The absence of any $\mathbb{Z}_2$ symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative $\epsilon$ expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supersymmetric Lee-Yang fixed point in three dimensions. We conjecture that the corresponding phase transition, if any, will be the first order transition.