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 $Z_N$-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.
Highlights
We study form factors of local and quasilocal operators in the two-dimensional complex sinh-Gordon model, which is a quantum version of the model introduced by Pohlmeyer–Lund–Regge [1,2] for negated coupling constant
In this note we show how to find form factors for the complex sinh-Gordon model following the algebraic approach proposed in [12,13,14]
It means that for large difference of two groups of rapidities each form factor of a (k, k) level operator factorizes into the product of form factors of a right (k, 0) level descendant operator over Vabq(x) and a left (0, k) level one
Summary
We study form factors of local and quasilocal operators in the two-dimensional complex sinh-Gordon model, which is a quantum version of the model introduced by Pohlmeyer–Lund–Regge [1,2] for negated coupling constant. In the case of descendant operators the reflection functions become matrices [16,18] Later we derive these properties for operators defined by their form factors. It can be shown that Vabq ∼ Φκmm , where the parameters a, b, q are related to κ, m, maccording to a m This identification [21] follows from the fact that the sine-Liouville model, i.e. the model described by the action (1.6) with λ = 0, is nothing but the SL(2, R)/U (1) coset conformal field theory, which is a noncompact (or negative real N ) counterpart of the ZN parafermion conformal models. Since the form factors of all primary operators and some descendant operators in the ZN Ising model are known explicitly [22,23,24,25], we may extend the corresponding expressions to the region g > 0.
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