Index-like theorem for massless fermions in spherically symmetric monopole backgrounds

Brennan, T. Daniel

doi:10.1007/jhep03(2022)095

Index-like theorem for massless fermions in spherically symmetric monopole backgrounds

Journal Article · Tue Mar 15 00:00:00 EDT 2022 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep03(2022)095· OSTI ID:1976456

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University of Chicago, IL (United States); Univ. of Chicago, IL (United States)

In this paper we study massless fermions coupled to spherically symmetric SU(N) monopoles without Yukawa couplings between the Higgs and fermion fields. The corresponding Dirac operator is not Fredholm and the associated eigenfunctions are not L²-normalizable. Here we derive a formula for the dimension of the plane-wave normalizable kernel of such a Dirac operator for fermions of any representation of SU(N) in the presence of any spherically symmetric monopole background. Notably, our results also apply to fermions coupled to monopoles that preserve non-abelian gauge symmetry.

View Accepted Manuscript (DOE)

Research Organization:: University of Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC); University of Chicago

Grant/Contract Number:: SC0009924

OSTI ID:: 1976456

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 3 Vol. 2022; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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