Universal Functions for Topological Correlators

Abstract

Abstract We consider correlation functions of topologically twisted, $$\mathcal {N}=2$$ N = 2 supersymmetric Yang–Mills theory with gauge group $$\textrm{SU}(2)$$ SU ( 2 ) and $$N_f\le 3$$ N f ≤ 3 massive hypermultiplets in the fundamental representation. For a smooth, oriented, closed four-manifold X with $$b_2^+>1$$ 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.