Abstract
We study the massless flows described by the staircase model introduced by Al.B. Zamolodchikov through the analytic continuation of the sinh-Gordon S-matrix, focusing on the renormalisation group flow from the tricritical to the critical Ising model. We show that the properly defined roaming limits of certain sinh-Gordon form factors are identical to the form factors of the order and disorder operators for the massless flow. As a by-product, we also construct form factors for a semi-local field in the sinh-Gordon model, which can be associated with the twist field in the ultraviolet limiting free massless bosonic theory.
Highlights
Group (RG) flow that passes by the successive conformal minimal models, eventually ending in a trivial IR fixed point which corresponds to a free massive Majorana fermion, i.e. the scaling Ising model
We study the massless flows described by the staircase model introduced by Al.B
We show that the properly defined roaming limits of certain sinh-Gordon form factors are identical to the form factors of the order and disorder operators for the massless flow
Summary
We discuss two-dimensional relativistically invariant quantum field theories. Form factors are matrix elements of (semi-)local operators O(x, t) between the vacuum and asymptotic states, i.e., FαO1,...,αn The asymptotic states correspond to multi-particle excitations, with dispersion relation (E, p) = (mαi cosh θ, mαi sinh θ), where αi indicates the particle species. In such models, any multi-particle state can be constructed from vacuum state by means of the particle creation operators A†αi(θ) by. With the massless creation and annihilation operators the asymptotic states can be written to the massive cases, and satisfy an algebra of the form (2.1) which can be obtained as the limit of the massive ZF algebra with S-matrices [13]. As the models considered in this paper have no bound states, (2.4)–(2.6) and (2.7) give all the constraints for form factors of general (semi-)local operators
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