Fixed points of semi-simple supersymmetric gauge theories

TL;DR

This paper analyzes fixed points and phase diagrams of semi-simple supersymmetric gauge theories, revealing new phenomena and classifying theories based on their conformal behavior and phase structure.

Contribution

It provides a comprehensive classification of superconformal fixed points in semi-simple SUSY gauge theories, including novel phenomena due to semi-simple interactions and residual effects.

Findings

Identification of all superconformal fixed points using field multiplicities.

Discovery of theories with residual interactions leading to asymptotic safety.

Classification of theories with diverse UV and IR behaviors.

Abstract

We study fixed points and phase diagrams of semi-simple supersymmetric gauge theories coupled to chiral superfields and a superpotential. Particular emphasis is put on new phenomena which arise due to the semi-simple nature of gauge interactions and the constraints dictated by supersymmetry, unitarity, and the $a$-theorem. Using field multiplicities as free parameters, we find all superconformal fixed points and classify theories according to their phase diagrams. Highlights include asymptotically free theories displaying a range of interacting fixed points in the IR, asymptotically non-free theories that become asymptotically safe due to residual interactions, UV-complete theories with gauge sectors that are simultaneously UV-free and IR-free, and theories that remain interacting both in the asymptotic UV and IR. Estimates for the sizes of conformal windows are also provided, and implications for model building are discussed.