Renormalization-group evolution and nonperturbative behavior of chiral gauge theories with fermions in higher-dimensional representations

Abstract

We study the ultraviolet to infrared evolution and nonperturbative behavior of a simple set of asymptotically free chiral gauge theories with an SU(N ) gauge group and an anomaly-free set of nS k copies of chiral fermions transforming as the symmetric rank-k tensor representation, S k , and nĀ ℓ copies of fermions transforming according to the conjugate antisymmetric rank-ℓ tensor representation,Ā ℓ , of this group with k, ℓ ≥ 2. As part of our study, we prove a general theorem guaranteeing that a low-energy effective theory resulting from the dynamical breaking of an anomalyfree chiral gauge theory is also anomaly-free. We analyze the theories with k = ℓ = 2 in detail and show that there are only a finite number of these. Depending on the specific theory, the ultraviolet to infrared evolution may lead to a non-Abelian Coulomb phase, or may involve confinement with massless composite fermions, or fermion condensation with dynamical gauge and global symmetry breaking. We show that S kĀk chiral gauge theories with k ≥ 3 are not asymptotically free. We also analyze theories with fermions in S k andĀ ℓ representations of SU(N ) with k = ℓ and k, ℓ ≥ 2.

If the weak were strong and the strong were weak

“…Early work on this topic is summarised in the review article [9]. Since then, a number of articles have studied the dynamics and phase structure of large classes of chiral gauge theories [10][11][12][13][14][15][16][17][18][19]. A number of proposals have been made for lattice regularisations of chiral gauge theories [20][21][22][23][24].…”

Quantum critical behavior of semisimple gauge theories

“…It is in addition a non-supersymmetric gauge-Yukawa theory that contains spin-0, spin- 1 2 as well as spin-1 particles. Whereas the literature contains investigations of the phase diagram of semi-simple and simple supersymmetric gauge theories [1][2][3], vector-like fermionic gauge theories [4][5][6][7][8][9][10][11][12], chiral gauge theories [13][14][15], Yukawa theories [16][17][18][19][20] and scalar theories [21] only very little has been done concerning the more general class of theories in which the Standard Model falls [22].…”

Dynamics and symmetries in chiral SU(N) gauge theories

“…The condensates (5.6) are of more general forms in those cases, with unequal values, and one or both of the symmetries SU(N) cf and SU(3) can be broken spontaneously. The set of the baryons B A,C and B [AB],m will continue to saturate the anomaly triangles of the remaining symmetries.6 (N ψ , N χ ) = (0, 1) Let us review the (N ψ , N χ ) = (0, 1) model studied in[3,8,9,10,13,1]. The matter fermions are χ[ij] ,η B j , B = 1, 2, .…”

“…13) with c j 's all different the Cartan subgroup of SU(N) c survives in the infrared. SU(2) f is broken.…”

“…See however[2]-[13] for partial list of earlier studies of these theories. See[14] for a recent work on the infrared fixed point in a class of chiral gauge theories.…”