The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations

Abstract

We study quasilocal operators in the quantum complex sinh-Gordon theory in the form factor approach. The free field procedure for descendant operators is developed by introducing the algebra of screening currents and related algebraic objects. We work out null vector equations in the space of operators. Further we apply the proposed algebraic structures to constructing form factors of the conserved currents $T_k$ and ${\Theta }_k$. We propose also form factors of current-current operators of the form $T_k{T}_{-l}$. Explicit computations of the four-particle form factors allow us to verify the recent conjecture of Smirnov and Zamolodchikov about the structure of the exact scattering matrix of an integrable theory perturbed by a combination of irrelevant operators. Our calculations confirm that such perturbations of the complex sinh-Gordon model and of the ${\mathbb{Z}}_N$ symmetric Ising models result in extra CDD factors in the $S$ matrix.

arXiv comment31 pages; v2: references added; v3: many misprints corrected

References in corpus (25)

• On space of integrable quantum field theories
• On the Operator Content of the Sinh-Gordon Model
• Asymptotic factorisation of form factors in two-dimensional quantum field theory
• Quantum scattering of charged solitons in the complex sine-Gordon model
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• Bosonic-type S-Matrix, Vacuum Instability and CDD Ambiguities
• Three-point Functions in Sine-Liouville Theory
• Fermionic structure in the sine-Gordon model: form factors and null-vectors
• Matrix elements of the operator T\bar{T} in integrable quantum field theory
• Free Field Construction for the ABF Models in Regime II
• Exact form factors for the scaling Z{N}-Ising and the affine A{N-1}-Toda quantum field theories
• $T\overline{T}$ deformations of non-Lorentz invariant field theories
• The composite operator T\bar{T} in sinh-Gordon and a series of massive minimal models
• Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory
• On scaling fields in $Z_N$ Ising models
• Form factors of descendant operators in the massive Lee-Yang model
• Functional Equations of Form Factors for Diagonal Scattering Theories
• Correlation functions of disorder fields and parafermionic currents in Z(N) Ising models
• Form factors in sinh- and sine-Gordon models, deformed Virasoro algebra, Macdonald polynomials and resonance identities
• On form factors and Macdonald polynomials
• Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality
• Form factors and action of U_{\sqrt{-1}}(sl_2~) on infinite-cycles
• Form factors of descendant operators: Resonance identities in the sinh-Gordon model
• Form factors of descendant operators: Reduction to perturbed $M(2,2s+1)$ models
• Algebraic approach to form factors in the complex sinh-Gordon theory

Cited by in corpus (5)

• Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs
• On correlation functions in $J\bar{T}$-deformed CFTs
• KdV charges in $T\bar{T}$ theories and new models with super-Hagedorn behavior
• Lattice models, deformed Virasoro algebra and reduction equation
• Scattering matrix for current-current deformations of the (2,2s+1) RSOS models