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 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, γχ χ, IR , combined with the conjectured critical condition, γχ χ, IR = 1 or equivalently γχ χ, IR (2−γχ χ, 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. *

Gauge/gravity dual dynamics for the strongly coupled sector of composite Higgs models

“…In a walking theory the dimension of the fermions in eq. (4.3) are lower at Λ U V and then the powers of Λ U V reduce (see for example [26,76] for discussion). Here, though, we will provide a new mechanism that allows an order one top Yukawa coupling as needed for the top mass.…”

Looking through the QCD conformal window with perturbation theory

“…x * 4.2 [9] (see also [10]). Previous analysis based on the perturbative series in the gauge-coupling found n * f ≈ 9 [11,12] for n c = 3, and using the Banks-Zaks conformal expansion found n * f ≈ 10 [13] or n * f ≈ 9 [14] for n c = 3, and x * ≈ 2.9 [14] in the Veneziano limit. 1 Lattice methods are the only ones so far based on first principles.…”

“…10 We will then assume in what follows that the conformal series (2.8) and (2.9) are all divergent asymptotic, consistently with our assumption about the coupling expansion. Even if IR renormalons might not occur, 7 Very recently the conformal expansion has been used to study the lower edge of the conformal window [13]. Assuming that γ equals exactly one at the lower edge, it has been found that n * f ≈ 10 in QCD.…”

“…Second, the condition γ = −1 applies possibly at large nc and corrections are expected at finite nc. Third, it is not clear how the loss of conformality is explained in the approach of [13], where conformality would seem to extend below n * f . 8 This is in agreement with the following fact.…”

“…12 The singularity t 0 might be in the negative real axis and due to a UV renormalon, though we cannot exclude the presence of other singularities off the real axis of unknown origin. 13 The scenario is summarized in figure 2. The first UV renormalon might occur at t 0 = −1/β 0 , in which case we would indeed have t 1 > |t 0 |.…”