Abstract
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 hierarchy associated with symmetry breaking in chiral gauge theories, which has no analogues in vector-like gauge theories such as QCD.
Highlights
Our world has a nontrivial chiral structure
Let us first examine the possibility that no condensates form, the system confines, and the flavor symmetry is unbroken [2]
This is in contrast to the (1,0) model which is reviewed in Sec
Summary
Our world has a nontrivial chiral structure. Macroscopic structures such as biological bodies often have approximately left-right symmetric forms, but not exactly. We shall restrict ourselves to various irreducibly chiral SUðNÞ theories, with Nψ fermions ψfijg in the symmetric representation, N χ fermions χ1⁄2ij in the antisymmetric representation, and a number of antifundamental (or fundamental) multiplets, ηAi (or ηAi).. We shall restrict ourselves to various irreducibly chiral SUðNÞ theories, with Nψ fermions ψfijg in the symmetric representation, N χ fermions χ1⁄2ij in the antisymmetric representation, and a number of antifundamental (or fundamental) multiplets, ηAi (or ηAi).3 The number of the latter is fixed by the condition that the gauge group be anomaly-free. They are not independent of each other, in view of the nonanomalous symmetries (2.4) The global continuous symmetry of the ψ − χ − η model is
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