On form factors and Macdonald polynomials

Abstract

We are developing the algebraic construction for form factors of local operators in the sinh-Gordon theory proposed in [B.Feigin, M.Lashkeivch, 2008]. We show that the operators corresponding to the null vectors in this construction are given by the degenerate Macdonald polynomials with rectangular partitions and the parameters $t=-q$ on the unit circle. We obtain an integral representation for the null vectors and discuss its simple applications.

13 pages; v2: eq. (4.1) corrected; v3: minor corrections, references added; v4: eq. (2.6) and the last equation of sect. 5 corrected; references updated; more minor corrections; v5: eq. (4.1) corrected again

References in corpus (3)

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

Cited by in corpus (6)

• Form factors in sinh- and sine-Gordon models, deformed Virasoro algebra, Macdonald polynomials and resonance identities
• 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
• Semiclassical approach to form factors in the sinh-Gordon model
• Note on four-particle form factors of operators $T_{2n}{T}_{-2n}$ in sinh-Gordon model