M & m Strings and Modular Forms

Abstract : We study relations between M-strings (one-dimensional intersections of M2-branes and M5-branes) in six dimensions and m-strings (magnetically charged monopole strings) in five dimensions. For specific configurations, we propose that the counting functions of BPS bound-states of M-strings capture the elliptic genus of the moduli space of m-strings. We check this proposal for the known cases, the Taub-NUT and Atiyah-Hitchin spaces for which we find complete agreement. Furthermore, we analyze the modular properties of the M-string free energies, which do not transform covariantly under SL(2,Z). However, for a given number of M-strings, we find that there exists a unique combination of unrefined genus-zero free energies that transforms as a Jacobi form under a congruence subgroup of SL(2,Z). These combinations correspond to summing over different numbers of M5-branes and make sense only if the distances between them are all equal. We explain that this is a necessary condition for the m-string moduli space to be factorizable into relative and center-of-mass parts.
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Physical Review D, American Physical Society, 2015, 92, pp.066005. 〈10.1103/PhysRevD.92.066005〉
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http://hal.in2p3.fr/in2p3-01155686
Contributeur : Sylvie Flores <>
Soumis le : mercredi 27 mai 2015 - 11:14:47
Dernière modification le : jeudi 8 février 2018 - 11:07:27

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S. Hohenegger, A. Iqbal, Soo-Jong Rey. M & m Strings and Modular Forms. Physical Review D, American Physical Society, 2015, 92, pp.066005. 〈10.1103/PhysRevD.92.066005〉. 〈in2p3-01155686〉

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