New anomalies, TQFTs, and confinement in bosonic chiral gauge theories

Abstract

We study a class of 4-dimensional SU(N) chiral gauge theories with fermions in the 2-index symmetric and antisymmetric representations and classify their infrared phases. The choice N = 4ℤ corresponds to gauging the fermion number and makes the theory purely bosonic. We examine the most general background fields of the centers of the gauge, non-abelian flavor, and U(1)-axial groups that can be consistently activated, thereby determine the faithful global continuous and discrete symmetries of the theory. This allows us to identify new mixed 0-form/1-form ‘t Hooft anomalies on both spin and nonspin manifolds. If the theory confines, the absence of composite fermions implies that continuous symmetries must be broken down to anomaly-free subgroups. Anomalies associated with discrete symmetries can be saturated either by breaking the symmetry or by a symmetry-preserving topological quantum field theory (TQFT). The latter, however, is obstructed on spin manifold. The interplay between these features greatly restricts the possible infrared physics. We present two examples that demonstrate our approach. We argue that if the theory confines, the zoo of anomalies and TQFT obstruction greatly restrict the viable infrared condensates. We also discuss the possibility that some theories flow to a conformal fixed point.

Dynamical Abelianization and anomalies in chiral gauge theories

“…In all of them, the conventional 't Hooft anomaly matching analysis is consistent with dynamical Abelianization hypothesis, and in some cases, the preliminary analysis involving the generalized symmetries and the mixed anomalies appears to give further support [17,36] for it. Still, in some of this class of models, the symmetry breaking pattern may be different from dynamical Abelianization, allowing for more general types of infrared gauge theories.…”

“…The results of the analysis, summarized in section 4.2, tell us that the proposed infrared physics, characterized by dynamical Abelianization, is consistent with the implications of the mixed anomalies and, perhaps, implied by them. The comparison between the implications of the mixed anomalies and those expected JHEP12(2022)110 (k being a common devisor of N − 4 and N + 4) studied recently [17,36].…”

“…The way this is done concretely has been explained in [20]- [36], by introducing the 1-form Z N gauge field, and imposing the condition (4.5) for a Z N gauge field. As our Z N center symmetry is a color-flavor locked symmetry, to render it properly a 1-form symmetry one must accompany the SU(N ) Wilson loop with a Ũ (1) holonomy (Aharonov-Bohm) loop for the fermions.…”

“…In the last few years some renewed efforts to understand better this class of gauge theories have been made [15]- [18], mainly by using the idea of anomaly-matching consistency requirement, both based on the conventional 't Hooft anomalies [19], and on the recently found generalized (e.g., 1-form) symmetries and mixed anomalies [20]- [36]. Also, the importance of the strong anomaly and its implications has been pointed out in the context of a large class of (generalized Bars-Yankielowicz and Georgi-Glashow) models, recently [37].…”

Semiclassics with ’t Hooft flux background for QCD with 2-index quarks

“…Recently, ref. [66] considers the 4d chiral gauge theories that contain both two-index symmetric and anti-symmetric Weyl fermions, and the anomaly matching constraint is studied in detail both on spin and non-spin manifolds. It would be fascinating if we can check those scenarios (even partially) by the reliable semiclassics with T 2 compactification, although the extension might not be straightforward due to the lack of the vector-like U(1) B symmetry.…”