Conformal Gauge-Yukawa Theories away From Four Dimensions

TL;DR

This paper explores the phase diagram and fixed points of Gauge-Yukawa theories in dimensions near four, revealing rich structures and fixed points that depend on the dimensionality, with implications for asymptotic safety and stability.

Contribution

It provides a detailed analysis of Gauge-Yukawa theories in d=4+ε dimensions, including fixed points and phase structure, extending previous work to a broader class of theories and dimensions.

Findings

Infrared fixed points emerge below four dimensions.

Ultraviolet fixed points appear above four dimensions.

Certain theories are asymptotically safe in higher dimensions.

Abstract

We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in $d=4+\epsilon$ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD$_d$ and then we add Yukawa interactions and scalars which we study at next-to- and next-to-next-to-leading order. Interacting infrared fixed points naturally emerge in dimensions lower than four while ultraviolet ones appear above four. We also analyse the stability of the scalar potential for the discovered fixed points. We argue for a very rich phase diagram in three dimensions while in dimensions higher than four certain Gauge-Yukawa theories are ultraviolet complete because of the emergence of an asymptotically safe fixed point.