Phases of supersymmetric O(N) theories

TL;DR

This paper investigates the phase structure of supersymmetric O(N) theories in three dimensions using renormalization group methods, revealing new features at strong coupling and resolving longstanding puzzles about degenerate phases.

Contribution

It provides an exact solution at infinite N, explores phase transitions at finite N, and uncovers a multi-valued superfield potential at strong coupling, advancing understanding of supersymmetric phase behavior.

Findings

Exact solution for infinite N case.

Identification of multi-valued superfield potential at strong coupling.

Discovery of a strongly-coupled fixed point affecting phase transitions.

Abstract

We perform a global renormalization group study of O(N) symmetric Wess-Zumino theories and their phases in three euclidean dimensions. At infinite N the theory is solved exactly. The phases and phase transitions are worked out for finite and infinite short-distance cutoffs. A distinctive new feature arises at strong coupling, where the effective superfield potential becomes multi-valued, signalled by divergences in the fermion-boson interaction. Our findings resolve the long-standing puzzle about the occurrence of degenerate O(N) symmetric phases. At finite N, we find a strongly-coupled fixed point in the local potential approximation and explain its impact on the phase transition. We also examine the possibility for a supersymmetric Bardeen-Moshe-Bander phenomenon, and relate our findings with the spontaneous breaking of supersymmetry in other models.