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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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http://hal.in2p3.fr/in2p3-01155686
Contributor : Sylvie Flores <>
Submitted on : Wednesday, May 27, 2015 - 11:14:47 AM
Last modification on : Tuesday, November 19, 2019 - 2:37:43 AM

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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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