我们对4维 SU(N) 2-指标手征规范理论进行了系统研究，并探讨了其忠实的全局对称性与动力学。这是一组有限的理论，其中的费米子处于2-指标对称与反对称表示中，且没有基本表示，它们不存在大 N 极限。我们结合微扰与非微扰方法，从而能够约束其红外（IR）相。具体而言，我们利用与连续和离散群相关的 't Hooft 反常排除了若干情形。在某些情形下，反常排除了费米子复合物的可能性。在其他情形下，连续与离散反常的相互作用导致了多个高阶凝聚，这些凝聚必然形成以匹配反常。此外，通过寻找匹配所有反常且产生最少 IR 自由度的凝聚，我们确定了最可能的对称性破缺模式。高圈 β 函数分析表明，少数理论可能流向共形不动点。
英文摘要：
We undertake a systematic study of the $4$-dimensional $SU(N)$ $2$-index chiral gauge theories and investigate their faithful global symmetries and dynamics. These are a finite set of theories with fermions in the $2$-index symmetric and anti-symmetric representations, with no fundamentals, and they do not admit a large-$N$ limit. We employ a combination of perturbative and nonperturbative methods, enabling us to constrain their infrared (IR) phases. Specifically, we leverage the 't Hooft anomalies associated with continuous and discrete groups to eliminate a few scenarios. In some cases, the anomalies rule out the possibility of fermion composites. In other cases, the interplay between the continuous and discrete anomalies leads to multiple higher-order condensates, which inevitably form to match the anomalies. Further, we pinpoint the most probable symmetry-breaking patterns by searching for condensates that match the full set of anomalies resulting in the smallest number of IR degrees of freedom. Higher-loop $β$-function analysis suggests that a few theories may flow to a conformal fixed point.
After many years of investigations, our understanding of the dynamics of strongly-coupled chiral gauge theories is still quite unsatisfactory today. Conventional wisdom about strongly-coupled gauge theories, successfully applied to QCD, is not always as useful in chiral gauge theories. Recently some new ideas and techniques have been developed, which involve concepts of generalized symmetries, of gauging a discrete center symmetry, and of generalizing the 't Hooft anomaly matching constraints to include certain mixed symmetries. This new development has been applied to chiral gauge theories, l…
Dynamics and symmetry realization in various chiral gauge theories in four dimensions are investigated, generalizing a recent work by M. Shifman and the present authors, by relying on the standard 't Hooft anomaly matching conditions and on some other general ideas. These requirements are so strong that the dynamics of the systems are severely constrained. Color-flavor or color-flavor-flavor locking, dynamical Abelianization, and combinations of these, are powerful ideas which often leads to solutions of the anomaly matching conditions. Moreover, a conjecture is made on generation of a mass hi…
We study two well-known $SU(N)$ chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work argues that these theories exhibit a subtle mod 2 anomaly, ruling out certain phases in which the theories confine without breaking their global symmetry, leaving a gapless composite fermion in the infra-red. We point out that no such anomaly exists. We further exhibit an explicit path to the gapless fermion phase, showing that there is no kinematic obstructi…
We present a simple argument which seems to favor, when applied to a large class of strongly-coupled chiral gauge theories, a dynamical-Higgs-phase scenario, characterized by certain bifermion condensates. Flavor symmetric confining vacua described in the infrared by a set of baryonlike massless composite fermions saturating the conventional 't Hooft anomaly matching equations, appear instead disfavored. Our basic criterion is that it should be possible to write a strong-anomaly effective action, analogous to the one used in QCD to describe the solution of the $U(1)_A$ problem in the low-energ…
Completely asymptotically free chiral theories with scalars
Sorbonne Université & CNRS（索邦大学与法国国家科学研究中心）；University of Southern Denmark（南丹麦大学）；Università di Napoli Federico II（那不勒斯费德里科二世大学）；INFN sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Scuola Superiore Meridionale（南方高等学院）
In this letter we uncover a new facet of chiral symmetry and the implications of its breaking in some theories. By generalizing the concept of chiral symmetry, tensor theories naturally arise. This novel approach adds to the known uses of tensor theories (quantum gravity, holography, entanglement,etc.) a possible link to QCD phenomena.
We demonstrate that $SO(N_{c})$ gauge theories with matter fields in the vector representation confine due to monopole condensation and break the $SU(N_{F})$ chiral symmetry to $SO(N_{F})$ via the quark bilinear. Our results are obtained by perturbing the ${\cal N}=1$ supersymmetric theory with anomaly-mediated supersymmetry breaking.
We study dynanics of $SU(N-4)$ gauge theories with fermions in rank-2 symmetric tensor and $N$ anti-fundamental representations, by perturbing supersymmetric theories with anomaly-mediated supersymmetry breaking. We find the $SU(N)\times U(1)$ global symmetry is dynamically broken to $SO(N)$ for $N\geq 17$, a different result from conjectures in the literature. For $N<17$, theories flow to infrared fixed points.
The axion particle may or may not exist, but the axion field can be used, as shown here, in an explicitly local formulation of a chiral U(1) gauge theory with both classical and quantum gauge invariance. Nonabelian analogues of axion fields, which have recently been introduced, can be used, together with their special symmetries, in a similar construction of nonabelian chiral gauge theories. As in known cases, the gauge symmetry is broken and the gauge boson acquires a mass by swallowing the axions which are therefore not physical in this construction.
We derive the finite one-loop counterterm required to restore the Ward Identities broken by the regularization scheme in chiral gauge theories. Our result is an analytic expression applicable to a wide class of regularizations satisfying a few general properties. We adopt the background field method, which ensures background gauge invariance in the quantized theory, and focus on renormalizable chiral theories with arbitrary gauge group and fermions in general representations. Our approach can be extended to theories involving scalars, such as the Standard Model, or to non-renormalizable theori…
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for $γ_5$. One goal is to show how chiral gauge theories can be renormalized despite the spurious breaking of gauge invariance and how to obtain the required symmetry-restoring counterterms. A second goal is to familiarize the reader with the theoretical basis of the renormalization of chiral gauge theories, the theorems that guarantee the existence of renormalized chiral gauge theories at all orders as consisten…
Chirality transfer between fermions and gauge fields plays a crucial role for understanding the dynamics of anomalous transport phenomena such as the Chiral Magnetic Effect. In this proceeding we present a first principles study of these processes based on classical-statistical real-time lattice simulations of strongly coupled QED $(e^2N_f=64)$. Our simulations demonstrate that a chirality imbalance in the fermion sector triggers chiral plasma instabilities in the gauge field sector, which ultimately lead to the generation of long range helical magnetic fields via a self-similar turbulent casc…
