Walking in the SU(N)

TL;DR

The paper maps the phase diagram of non-supersymmetric SU($N$) gauge theories with fermions in higher-dimensional representations, highlighting how representation-dependent screening alters the conformal window and walking behavior. It employs the two-loop $\beta$-function and chiral-symmetry breaking criteria to delineate regions of asymptotic freedom, Banks–Zaks fixed points, and conformality, then assesses realistic walking technicolour candidates under electroweak precision and anomaly constraints. The authors identify prime and alternative walking models across representations (F, G, $S_2$, $A_2$, adjoint, etc.), including partially gauged and split technicolour scenarios, and discuss their phenomenological implications, such as the $S$ parameter and potential dark matter sectors. They further refine the near-conformal spectrum, arguing for the possible emergence of light composite scalars near the fixed point and connecting these insights to the viability of dynamical electroweak symmetry breaking with controllable EW corrections.

Abstract

We study the phase diagram as function of the number of colours and flavours of asymptotically free non-supersymmetric theories with matter in higher dimensional representations of arbitrary SU(N) gauge groups. Since matter in higher dimensional representations screens more than in the fundamental a general feature is that a lower number of flavours is needed to achieve a near-conformal theory. We study the spectrum of the theories near the fixed point and consider possible applications of our analysis to the dynamical breaking of the electroweak symmetry.

Figures (2)

• Figure 1: Phase diagram for theories with fermions in the (from top to bottom in the plot; colour online): i) fundamental representation (grey), ii) two-index antisymmetric (blue), iii) two-index symmetric (red), iv) adjoint representation (green) as a function of the number of flavours and the number of colours. The shaded areas depict the corresponding conformal windows. The upper solid curve represents $N_f^\mathrm{I}[R(N)]$ (loss of asymptotic freedom), the lower $N_f^\mathrm{II}[R(N)]$ (loss of chiral symmetry breaking). The dashed curves show $N_f^\mathrm{III}[R(N)]$ (existence of a Banks--Zaks fixed point). Note how consistently the various representations merge into each other when, for a specific value of $N$, they are actually the same representation.
• Figure 2: Technicolour models. The boxes depict under which gauge groups the different particles transform. The box headlined "SM" represents all standard model particles (excluding an elementary Higgs). N and E stand for a fourth family of leptons, which may or may not have to be included in order to evade a topological Witten anomaly. They have to be included, if the number of techniquark families transforming under the electroweak symmetry times the number of colour degrees of freedom is an odd number. Left panel: In fully gauged technicolour models, all techniquarks transform under the electroweak symmetry. Right panel: In partially gauged technicolour a part of the techniquarks are electroweak singlets. It is conceivable that only one (maximal splitting) or several (sub-maximal splitting) families of techniquarks carry electroweak charges. The latter set-up may be an alternative cure from the Witten anomaly not involving additional leptons.