Into the conformal window: multi-representation gauge theories

Abstract

We investigate the conformal window of four-dimensional gauge theories with fermionic matter fields in multiple representations. Of particularly relevant examples are the ultra-violet complete models with fermions in two distinct representations considered in the context of composite Higgs and top partial-compositeness. We first discuss various analytical approaches to unveil the lower edge of the conformal window and their extension to the multiple matter representations. In particular, we argue that the scheme-independent series expansion for the anomalous dimension of a fermion bilinear at an infrared fixed point, ${\gamma }_{\bar{\chi }\chi ,\mathrm{IR}}$, combined with the conjectured critical condition, ${\gamma }_{\bar{\chi }\chi ,\mathrm{IR}}=1$ or equivalently ${\gamma }_{\bar{\chi }\chi ,\mathrm{IR}}(2-{\gamma }_{\bar{\chi }\chi ,\mathrm{IR}})=1$, can be used to determine the boundary of conformal phase transition on fully physical grounds. In illustrative cases of $SU(2)$ and $SU(3)$ theories with $N_R$ Dirac fermions in various representations, we assess our results by comparing to other analytical or lattice results.

arXiv comment39 pages, 8 figures, 8 tables; Revised version; To appear in PRD

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• Infrared fixed point and anomalous dimensions in a composite Higgs model
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• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Center vortices and the $\mathrm{SU}(3)$ conformal window
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• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory