In principle, there is no obstacle to gapping fermions preserving any global symmetry that does not suffer a ’t Hooft anomaly. In practice, preserving a symmetry that is realized on fermions in a chiral manner necessitates some dynamics beyond simple quadratic mass terms. We show how this can be achieved using familiar results about the strong coupling dynamics of supersymmetric gauge theories and, in particular, the phenomenon of confinement without chiral symmetry breaking. We present simple models that gap fermions while preserving a symmetry group under which they transform in chiral representations. For example, we show how to gap a collection of 4D fermions that carry the quantum numbers of one generation of the standard model, but without breaking electroweak symmetry. We further show how to gap fermions in groups of 16 while preserving certain discrete symmetries that exhibit a mod 16 anomaly.

中文翻译：

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缺口手性费米子

原则上，保持费米子不存在任何障碍，可以保持任何不会出现't Hooft异常的全局对称性。在实践中，要保持以手性方式在费米子上实现的对称性，除了简单的二次质量项外，还需要一些动力学。我们展示了如何使用有关超对称规范理论的强耦合动力学的熟悉结果，尤其是没有手性对称性破坏的局限现象，可以实现这一目标。我们提出了一些简单的模型，这些模型能使费米缺口同时保留一个对称基团，并在此对称基团下转化手性表示形式。例如，我们展示了如何在不破坏电弱对称性的情况下，使带有一代标准模型量子数的4D费米子缺口。