Perturbative tests of non-perturbative counting

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We observe that a class of quarter-BPS dyons in \( \mathcal{N} = 4 \) theories with charge vector (Q, P) and with nontrivial values of the arithmetic duality invariant I := gcd(QP) are nonperturbative in one frame but perturbative in another frame. This observation suggests a test of the recently computed nonperturbative partition functions for dyons with nontrivial values of the arithmetic invariant. For all values of I, we show that the nonperturbative counting yields vanishing indexed degeneracy for this class of states everywhere in the moduli space in precise agreement with the perturbative result.


Black Holes in String Theory Superstrings and Heterotic Strings String Duality 


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© The Author(s) 2010

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique et Hautes Energies (LPTHE)Université Pierre et Marie Curie-Paris 6; CNRS UMR 7589Paris Cedex 05France
  2. 2.Department of Theoretical PhysicsTata Institute of Fundamental ResearchMumbaiIndia

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