Résumé |
I study BPS excitations in M5-M2-brane configurations with a compact transverse direction, which are also
relevant for type IIa and IIb little string theories. These configurations are dual to a class of toric elliptically
fibered Calabi-Yau manifolds $X_N$ with manifest $SL(2,\mathbb{Z})\times SL(2,\mathbb{Z})$ modular
symmetry. They admit two dual gauge theory descriptions. For both, the non-perturbative partition function
can be written as an expansion of the topological string partition function of $X_N$ with respect to either of
the two modular parameters. I analyse the resulting BPS counting functions in detail and unravel a number of
remarkable relations. In particular, I find that for certain M2-brane configurations, the free energies in the two
dual theories agree with each other. This points to a new correspondence between instanton and monopole
configurations and is also a manifestation of T-duality between type IIa and IIb little string theories. Finally, I
briefly comment on a generalisation of these results to orbifolds of little string theories. |