Remarks on twisted theories with matter

TL;DR

This paper explores N=2 twisted gauge theories with matter, deriving a blowup formula involving hyperelliptic sigma-functions and revealing identities between hyperelliptic Theta functions.

Contribution

It provides a consistent formulation of twisted theories with matter on four-manifolds and explicitly derives the blowup formula using hyperelliptic sigma-functions.

Findings

Blowup formula expressed via hyperelliptic sigma-functions

Explicit magnetic flux configuration for SU(2k)

Identities between hyperelliptic Theta functions

Abstract

We investigate some aspects of N=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(2k). We obtain the blowup formula and show that the blowup function is given by a hyperelliptic sigma-function with singular characteristic. We compute the contact terms and find, as a corollary, interesting identities between hyperelliptic Theta functions.