Form factors in sinh- and sine-Gordon models, deformed Virasoro algebra, Macdonald polynomials and resonance identities

Abstract

We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [arXiv:0812.4776]. We find the algebraic construction to be related to a particular limit of the tensor product of the deformed Virasoro algebra and a suitably chosen Heisenberg algebra. To analyze the space of local operators in the framework of the form factor formalism we introduce screening operators and construct singular and cosingular vectors in the Fock spaces related to the free field realization of the obtained algebra. We show that the singular vectors are expressed in terms of the degenerate Macdonald polynomials with rectangular partitions. We study the matrix elements that contain a singular vector in one chirality and a cosingular vector in the other chirality and find them to lead to the resonance identities already known in the conformal perturbation theory. Besides, we give a new derivation of the equation of motion in the sinh-Gordon theory, and a new representation for conserved currents.

29 pages, no figures; v2: (2.47), (3.5) corrected; v3: miscorrected (2.47) reverted; references corrected; v4: misprints and negligible mistakes corrected; references updated; v5: for so long unnoticed mistake in (2.50) corrected

References in corpus (2)

• Fermionic structure in the sine-Gordon model: form factors and null-vectors
• On form factors and Macdonald polynomials

Cited by in corpus (9)

• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Approaching the Self-Dual Point of the Sinh-Gordon model
• The complex sinh-Gordon model: form factors of descendant operators and current-current perturbations
• 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
• (p,q)-deformed Virasoro-Witt n-algebra
• Lattice models, deformed Virasoro algebra and reduction equation
• Note on four-particle form factors of operators $T_{2n}{T}_{-2n}$ in sinh-Gordon model
• Semiclassical approach to form factors in the sinh-Gordon model