Hidden symmetries in two dimensional field theory

Michael Creutz

doi:10.1016/j.aop.2006.01.003

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arXiv · hep-th/0508116

Hidden symmetries in two dimensional field theory

Michael Creutz

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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 $SU(2)\times SU(2)$ chiral symmetry in this trivial theory. I then discuss in what sense this field should be interpreted as a Goldstone boson.

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Michael Creutz. 2006-01-31. Hidden symmetries in two dimensional field theory. https://doi.org/10.1016/j.aop.2006.01.003

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