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The Chiral Space of Local Operators in SU(2)-Invariant Thirring Model

Atsushi Nakayashiki

Published Jan 1, 2003• 5 citations
OpenAlex

Abstract

The space of local operators in the SU(2) invariant Thirring model (SU(2) ITM) is studied by the form factor bootstrap method. By constructing sets of form factors explicitly we define a susbspace of operators which has the same character as the level one integrable highest weight representation of ̂ sl2. This makes a correspondence between this subspace and the chiral space of local operators in the underlying conformal field theory, the su(2) Wess-Zumino-Witten model at level one. 1

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The space of local operators in the SU(2) invariant Thirring model (SU(2) ITM) is studied by the form factor bootstrap method. By constructing sets of form factors explicitly we define a susbspace of operators which has the same character as the level one integrable highest weight representation of ̂ sl2. This makes a correspondence between this subspace and the chiral space of local operators in the underlying conformal field theory, the su(2) Wess-Zumino-Witten model at level one. 1
Dedicated to the memory of Moshé Flato The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (“replica”) deformation of the form factor approach. We show that replicadeformed form factors of the SU(2)-invariant Thirring model can be found among the solutions of the rational sl2-type quantum Knizhnik-Zamolodchikov equation at generic level. We show that modulo conserved charge solutions the deformed form factors are in one-to-one correspondence to the ones at level zero and use this to conjecture the deformed form factors of the Noether The form factor approach to massive integrable quantum field theories (QFTs) [9, 20] provides a powerful tool to compute exact matrix elements of local operators from the knowledge of the (factorized) S-matrix. To be precise, a form factor in this context is the matrix element of some local operator between the physical vacuum and a multi-particle