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Factorization of N=2 theories partition functions on the squashed 3-sphere

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Mathematics and Applications of Branes in String and M-theory

We show that partition functions of N=2 theories on the squashed 3-sphere can be factorized into pairs of vortex theories defined on the two copies of R^2 x S1, corresponding to the two degeneration limits of the ellipsoid. We comment on how the ellipsoid partition function appears to provide the modular invariant non-perturbative completion of the vortex theory. We conclude with the geometrical engineering of the vortex theory.

This talk is part of the Isaac Newton Institute Seminar Series series.

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