Non-supersymmetric cousins of supersymmetric gauge theories: quantum space of parameters and double scaling limits

TL;DR

This paper explores non-supersymmetric two-dimensional sigma models, revealing their similarities to supersymmetric gauge theories, including quantum corrections, dualities, and phase transitions, and introduces a double scaling limit involving branched polymers.

Contribution

It demonstrates that non-supersymmetric sigma models share key properties with supersymmetric theories and introduces a double scaling limit to describe their singularities.

Findings

Quantum corrections to mass parameters analogous to supersymmetric moduli spaces

Existence of massless solitons and bound states

Rearrangement of stable states spectrum from weak to strong coupling

Abstract

I point out that standard two dimensional, asymptotically free, non-linear sigma models, supplemented with terms giving a mass to the would-be Goldstone bosons, share many properties with four dimensional supersymmetric gauge theories, and are tractable even in the non-supersymmetric cases. The space of mass parameters gets quantum corrections analogous to what was found on the moduli space of the supersymmetric gauge theories. I focus on a simple purely bosonic example exhibiting many interesting phenomena: massless solitons and bound states, Argyres-Douglas-like CFTs and duality in the infrared, and rearrangement of the spectrum of stable states from weak to strong coupling. At the singularities on the space of parameters, the model can be described by a continuous theory of randomly branched polymers, which is defined beyond perturbation theory by taking an appropriate double scaling limit.