Analytic index and chiral fermions

A recent application of an index relation of the form, $dim\ ker\ M - dim\ ker\ M^{\dagger} = ν$, to the generation of chiral fermions in a vector-like gauge theory is reviewed. In this scheme the chiral structure arises from a mass term with a non-trivial index.The essence of the generalized Pauli-Villars regularization of chiral gauge theory, which is based on this mechanism, is also clarified.

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