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Asymptotic mass degeneracies in conformal field theories.(English)Zbl 0703.17015

From the paper: “By applying a method of Hardy and Ramanujan to characters of rational conformal field theories, we find an asymptotic expansion for degeneracy of states in the limit of large mass which is exact for strings propagating in more than wo uncompactified space-time dimensions. Moreover, we explore how the rationality of the conformal field theory is reflected in the degeneracy of the states. We also consider the one loop partition function for strings, restricted to physical states, for arbitrary (irrational) conformal theories, and obtain an asymptotic expansion for it in the limit that the torus degenerates. This expansion depends only on the spectrum of (physical and unphysical) relevant operators in the theory. We see how rationality is consistent with the smoothness of mass degeneracies as a function of moduli.”
Reviewer: A.N.Pressley

MSC:

17B65 Infinite-dimensional Lie (super)algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

Cite

References:

[1]Hagedorn, R.: Nuovo Cimento [Suppl.]3, 147 (1965)
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[4]Dijkgraaf, R. Verlinde, E.: to appear in the proceedings of Annecy Conference on Conformal Field Theory, 1988 ·Zbl 0958.81510
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[7]Andrews, G. E.: Theory of partitions, encyclopedia of mathematics and its applications, vol. 2. Reading, M. A.: Addison Wesley 1976
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[9]Cardy, J.: Nucl. Phys.B205, 17 (1982) ·doi:10.1016/0550-3213(82)90464-3
[10]Chandrasekharan, K.: Elliptic functions. Berlin, Heidelberg, New York: Springer 1985 ·Zbl 0575.33001
[11]Zamolodchikov, A. B.: JETP Lett.43, 731 (1986); Sov. J. Nucl. Phys.46, 1090 (1987)
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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.
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