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Asymptotic mass degeneracies in conformal field theories

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Abstract

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 isexact for strings propagating in more than two uncompactified space-time dimensions. Moreover we explore how the rationality of the conformal theory is reflected in the degeneracy of 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.

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Authors and Affiliations

  1. Department of Theoretical Physics, University of Oxford, OX1 3NP, Oxford, UK

    Iraj Kani

  2. Lyman Laboratory of Physics, Harvard University, 02138, Cambridge, MA, USA

    Cumrun Vafa

Authors
  1. Iraj Kani
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  2. Cumrun Vafa
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Communicated by A. Jaffe

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Kani, I., Vafa, C. Asymptotic mass degeneracies in conformal field theories. Commun.Math. Phys. 130, 529–580 (1990). https://doi.org/10.1007/BF02096934

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  • DOI: https://doi.org/10.1007/BF02096934

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