Remarks on Twisted Theories with Matter

We investigate some aspects of = 2 twisted theories with matter hypermultiplets in the fundamental representation of the gauge group. A consistent formulation of these theories on a general four-manifold requires turning on a particular magnetic flux, which we write down explicitly in the case of SU(2l). We obtain the blowup formula and show that the blowup function is given by a hyperelliptic σ-function with singular characteristic. We compute the contact terms and find, as a corollary, interesting identities between hyperelliptic Theta functions.

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