Into the conformal window: Multirepresentation 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 ultraviolet 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, ${\ensuremath{\gamma}}_{\overline{\ensuremath{\chi}}\ensuremath{\chi},\mathrm{IR}}$, combined with the conjectured critical condition, ${\ensuremath{\gamma}}_{\overline{\ensuremath{\chi}}\ensuremath{\chi},\mathrm{IR}}=1$ or equivalently ${\ensuremath{\gamma}}_{\overline{\ensuremath{\chi}}\ensuremath{\chi},\mathrm{IR}}(2\ensuremath{-}{\ensuremath{\gamma}}_{\overline{\ensuremath{\chi}}\ensuremath{\chi},\mathrm{IR}})=1$, 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.