Universal Functions for Topological Correlators

We consider correlation functions of topologically twisted, N=2 N = 2 supersymmetric Yang–Mills theory with gauge group SU(2) SU ( 2 ) and Nf≤ 3 N f ≤ 3 massive hypermultiplets in the fundamental representation. For a smooth, oriented, closed four-manifold X with b₂⁺>1 b 2 + > 1 , the correlation functions are expressed in terms of a finite set of universal functions. The mass dependence of these functions encodes intersection numbers of the moduli space of instantons. We determine closed expressions for the universal functions by combining techniques of the Seiberg–Witten geometry, the u -plane integral, and the blowup formula. If X is specialised to a complex algebraic surface S , the correlation functions can be identified with generating functions of Segre invariants for moduli spaces of sheaves on S . With appropriate identifications of parameters, we establish agreement of our results with results by Göttsche and Kool for these generating functions.