English

Hidden symmetries in two dimensional field theory

High Energy Physics - Theory 2009-11-11 v2 High Energy Physics - Lattice

Abstract

The bosonization process elegantly shows the equivalence of massless scalar and fermion fields in two space-time dimensions. However, with multiple fermions the technique often obscures global symmetries. Witten's non-Abelian bosonization makes these symmetries explicit, but at the expense of a somewhat complicated bosonic action. Frenkel and Kac have presented an intricate mathematical formalism relating the various approaches. Here I reduce these arguments to the simplest case of a single massless scalar field. In particular, using only elementary quantum field theory concepts, I expose a hidden SU(2)×SU(2)SU(2)\times SU(2) chiral symmetry in this trivial theory. I then discuss in what sense this field should be interpreted as a Goldstone boson.

Keywords

Cite

@article{arxiv.hep-th/0508116,
  title  = {Hidden symmetries in two dimensional field theory},
  author = {Michael Creutz},
  journal= {arXiv preprint arXiv:hep-th/0508116},
  year   = {2009}
}

Comments

15 pages. Revision adds numerous references and puts things in better historical context

R2 v1 2026-07-22T15:31:37.829Z