zbMATH — the first resource for mathematics

On form factors and Macdonald polynomials. (English) Zbl 1342.81187
Summary: We are developing the algebraic construction for form factors of local operators in the sinh-Gordon theory proposed by B. Feigin and the first author [J. Phys. A, Math. Theor. 42, No. 30, Article ID 304014, 32 p. (2009; Zbl 1177.81121)]. 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.

81R12 Groups and algebras in quantum theory and relations with integrable systems
05E05 Symmetric functions and generalizations
33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
Full Text: DOI arXiv
[1] Feigin, B.; Lashkevich, M., Form factors of descendant operators: free field construction and reflection relations, J. Phys., A 42, 304014, (2009) · Zbl 1177.81121
[2] Belavin, A.; Polyakov, AM; Zamolodchikov, A., Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys., B 241, 333, (1984) · Zbl 0661.17013
[3] A.B. Zamolodchikov and Al.B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys.B 477 (1996) 577 [hep-th/9506136] [INSPIRE]. · Zbl 0925.81301
[4] Awata, H.; Matsuo, Y.; Odake, S.; Shiraishi, J., Collective field theory, Calogero-Sutherland model and generalized matrix models, Phys. Lett., B 347, 49, (1995) · Zbl 0894.17027
[5] Al. Zamolodchikov, Two point correlation function in scaling Lee-Yang model, Nucl. Phys.B 348 (1991) 619 [INSPIRE].
[6] Al. Zamolodchikov, Higher equations of motion in Liouville field theory, Int. J. Mod. Phys.A 19S2 (2004) 510 [hep-th/0312279] [INSPIRE]. · Zbl 1080.81062
[7] Lashkevich, M., Resonances in sinh- and sine-Gordon models and higher equations of motion in Liouville theory, J. Phys., A 45, 455403, (2012) · Zbl 1267.81276
[8] Lukyanov, SL; Zamolodchikov, AB, Exact expectation values of local fields in quantum sine-Gordon model, Nucl. Phys., B 493, 571, (1997) · Zbl 0909.58064
[9] Karowski, M.; Weisz, P., Exact form-factors in (1 + 1)-dimensional field theoretic models with soliton behavior, Nucl. Phys., B 139, 455, (1978)
[10] Smirnov, FA, Form-factors in completely integrable models of quantum field theory, Adv. Ser. Math. Phys., 14, 1, (1992)
[11] Koubek, A.; Mussardo, G., On the operator content of the sinh-Gordon model, Phys. Lett., B 311, 193, (1993)
[12] Lukyanov, SL, Form-factors of exponential fields in the sine-Gordon model, Mod. Phys. Lett., A 12, 2543, (1997) · Zbl 0902.35099
[13] Cardy, JL; Mussardo, G., Form-factors of descendent operators in perturbed conformal field theories, Nucl. Phys., B 340, 387, (1990)
[14] Koubek, A., A method to determine the operator content of perturbed conformal field theories, Phys. Lett., B 346, 275, (1995)
[15] Babelon, O.; Bernard, D.; Smirnov, F., Quantization of solitons and the restricted sine-Gordon model, Commun. Math. Phys., 182, 319, (1996) · Zbl 0877.58029
[16] Babelon, O.; Bernard, D.; Smirnov, F., Null vectors in integrable field theory, Commun. Math. Phys., 186, 601, (1997) · Zbl 0878.35097
[17] Jimbo, M.; Miwa, T.; Takeyama, Y., Counting minimal form-factors of the restricted sine-Gordon model, Moscow Math. J., 4, 787, (2004) · Zbl 1084.81066
[18] Jimbo, M.; Miwa, T.; Mukhin, E.; Takeyama, Y., Form-factors and action of \( \text{U}\left( {-{1^{{{1 \left/ {2} \right.}}}}} \right)\left( {\widetilde{\text{sl}}(2)} \right) \) on infinite cycles, Commun. Math. Phys., 245, 551, (2004) · Zbl 1106.81044
[19] Delfino, G.; Niccoli, G., Form-factors of descendant operators in the massive Lee-Yang model, J. Stat. Mech., 0504, (2005)
[20] Delfino, G.; Niccoli, G., Isomorphism of critical and off-critical operator spaces in two-dimensional quantum field theory, Nucl. Phys., B 799, 364, (2008) · Zbl 1292.81123
[21] Jimbo, M.; Miwa, T.; Smirnov, F., Hidden Grassmann structure in the XXZ model V: sine-Gordon model, Lett. Math. Phys., 96, 325, (2011) · Zbl 1214.81249
[22] Jimbo, M.; Miwa, T.; Smirnov, F., Fermionic structure in the sine-Gordon model: form factors and null-vectors, Nucl. Phys., B 852, 390, (2011) · Zbl 1229.81171
[23] A.A. Belavin, V.A. Belavin, A.V. Litvinov, Y.P. Pugai and Al.B. Zamolodchikov, On correlation functions in the perturbed minimal models M (2\(,\) 2\(n\) + 1), Nucl. Phys.B 676 (2004) 587 [hep-th/0309137] [INSPIRE]. · Zbl 1089.81037
[24] Fateev, VA; Postnikov, VV; Pugai, YP, On scaling fields in Z_{N} Ising models, JETP Lett., 83, 172, (2006)
[25] Fateev, VA; Pugai, YP, Correlation functions of disorder fields and parafermionic currents in Z_{N} Ising models, J. Phys., A 42, 304013, (2009) · Zbl 1179.82028
[26] Fring, A.; Mussardo, G.; Simonetti, P., Form-factors for integrable Lagrangian field theories, the sinh-Gordon theory, Nucl. Phys., B 393, 413, (1993) · Zbl 1245.81238
[27] Shiraishi, J.; Kubo, H.; Awata, H.; Odake, S., A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions, Lett. Math. Phys., 38, 33, (1996) · Zbl 0867.17010
[28] Lukyanov, S.; Pugai, Y., Bosonization of ZF algebras: direction toward deformed Virasoro algebra, J. Exp. Theor. Phys., 82, 1021, (1996)
[29] Delfino, G.; Niccoli, G., The composite operator \( T\overline{T} \) in sinh-Gordon and a series of massive minimal models, JHEP, 05, 035, (2006)
[30] I.G. Macdonald, Symmetric functions and hall polynomials, 2\^{nd} edition, Oxford University Press, Oxford U.K. (1995). · Zbl 0824.05059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.