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arXiv:1610.04926 · Physics Letters B

Algebraic approach to form factors in the complex sinh-Gordon theory

Michael Lashkevich, Yaroslav Pugai

Published Nov 22, 2016• 1 citation
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Abstract

We study form factors of the quantum complex sinh-Gordon theory in the algebraic approach. In the case of exponential fields the form factors can be obtained from the known form factors of the ZN-symmetric Ising model. The algebraic construction also provides an Ansatz for form factors of descendant operators. We obtain generating functions of such form factors and establish their main properties: the cluster factorization and reflection equations.

DOI
10.1016/j.physletb.2016.11.031

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We study form factors of the quantum complex sinh-Gordon theory in the algebraic approach. In the case of exponential fields the form factors can be obtained from the known form factors of the ZN-symmetric Ising model. The algebraic construction also provides an Ansatz for form factors of descendant operators. We obtain generating functions of such form factors and establish their main properties: the cluster factorization and reflection equations.
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We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic limit of the S-matrix of a field theory, and when there is a well-defined mapping between the Hilbert spaces and operators of the two theories. This correspondence provides an efficient method to compute matrix elements of Bethe Ansatz integrable models, overpassing the technical difficulties of their direct determination. We analyze this correspondence for the simplest example in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon models.
We study the space of scaling fields in the Z N symmetric models with factorized scattering and propose the simplest algebraic relations between the form factors induced by the action of deformed parafermionic currents. The construction gives a new free field representation for form factors of perturbed Virasoro algebra primary fields, which are parafermionic algebra descendants. We find exact vacuum expectation values of physically important fields and study the correlation functions of order and disorder fields in the form factor and conformal field theories perturbation approaches.
The purpose of the "bootstrap program" for integrable quantum field theories in 1+1 dimensions is to construct explicitly a model in terms of its Wightman functions.In this article, this program is mainly illustrated in terms of the sinh-Gordon model and the SU (N ) Gross-Neveu model.The nested off-shell Bethe ansatz for an SU (N ) factorizing S-matrix is constructed.We review some previous results on sinh-Gordon form factors and the quantum operator field equation.The problem of how to sum over intermediate states is considered in the short distance limit of the two point Wightman function for the sinh-Gordon model.