Canonical non-Abelian dual transformations in supersymmetric field theories

Thomas Curtright, Cosmas Zachos

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22 Citations (Scopus)

Abstract

A generating functional F is found for a canonical non-Abelian dual transformation which maps the supersymmetric chiral O(4) σ model to an equivalent supersymmetric extension of the dual σ model. This F produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation, and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a symphysis of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional T which relates wave functions in the two quantum theories is argued to be exactly given by T=exp(iF).

Original languageEnglish (US)
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume52
Issue number2
DOIs
StatePublished - 1995

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fermions
tangents
quantum theory
curvature
wave functions

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

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AB - A generating functional F is found for a canonical non-Abelian dual transformation which maps the supersymmetric chiral O(4) σ model to an equivalent supersymmetric extension of the dual σ model. This F produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation, and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a symphysis of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional T which relates wave functions in the two quantum theories is argued to be exactly given by T=exp(iF).

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