The critical \(\text{O}(N)\) \(\sigma\)-model at dimensions \(2<d<4\): Fusion coefficients and anomalous dimensions. (English) Zbl 0941.81585

Summary: Fusion coefficients and anomalous dimensions of the quasi-primary fields are extracted from the \(1/N\) expansion using representation theory of the conformal group whose formulae are analytically extended to \(2<d<4\).


81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
22E70 Applications of Lie groups to the sciences; explicit representations
Full Text: DOI


[1] Lang, K.; Rühl, W., Z. Phys., C50, 285 (1991)
[2] Lang, K.; Rühl, W., Z. Phys., C51, 127 (1991)
[3] Lang, K.; Rühl, W., Nucl. Phys., B377, 371 (1992)
[4] Lang, K.; Rühl, W., Phys. Lett., B275, 93 (1992)
[5] Lang, K.; Rühl, W., The critical \(O(N)\) σ-model at dimensions \(2 < d < 4\): A list of quasiprimary fields, Kaiserslautern University preprint KL-TH-92/7 (May 1992)
[6] Vasil’ev, A. N.; Pismak, Yu. M.; Khonkonen, Yu. R., Theor. Mat. Fiz., 47, 291 (1981)
[7] Vasil’ev, A. N.; Pismak, Yu. M.; Khonkonen, Yu. R., Theor. Mat. Fiz., 50, 195 (1982)
[8] Bernreuther, W.; Wegner, F., Phys. Rev. Lett., 57, 1383 (1986)
[9] Dobrev, V. K.; Mack, G.; Petkova, V. B.; Petrova, S. G.; Todorov, I. T., Harmonic analysis on the \(n\)-dimensional Lorentz group and its application to conformal quantum field theory, (Lecture Notes in Physics, vol. 63 (1977), Springer: Springer Berlin) · Zbl 0407.43010
[10] Abe, R.; Hikami, S., Prog. Theor. Phys., 49, 1851 (1973)
[11] Gradshteyn, I. S.; Ryzhik, I. M., Table of integrals, series and products (1965), Academic Press: Academic Press New York · Zbl 0918.65002
[12] Luke, Y. L., The special functions and their approximations (1969), Academic Press: Academic Press New York, 2 Vols. · Zbl 0193.01701
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.