Topology and strong four fermion interactions in four dimensions

Simon Catterall, Nouman Butt

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We study massless fermions interacting through a particular four-fermion term in four dimensions. Exact symmetries prevent the generation of bilinear fermion mass terms. We determine the structure of the low-energy effective action for the auxiliary field needed to generate the four-fermion term and find it has an novel structure that admits topologically nontrivial defects with nonzero Hopf invariant. We show that fermions propagating in such a background pick up a mass without breaking symmetries. Furthermore, pairs of such defects experience a logarithmic interaction. We argue that a phase transition separates a phase where these defects proliferate from a broken phase where they are bound tightly. We conjecture that, by tuning one additional operator, the broken phase can be eliminated with a single BKT-like phase transition separating the massless from massive phases.

Original languageEnglish (US)
Article number094502
JournalPhysical Review D
Issue number9
StatePublished - May 1 2018

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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