Mocking the u-plane integral

Georgios Korpas, Jan Manschot, Gregory W. Moore, Iurii Nidaiev

Research output: Contribution to journalArticlepeer-review


The u-plane integral is the contribution of the Coulomb branch to correlation functions of N= 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group SU (2) , for an arbitrary four-manifold with (b1,b2+)=(0,1). The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

Original languageEnglish (US)
Article number43
JournalResearch in Mathematical Sciences
Issue number3
StatePublished - Sep 2021

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)
  • Computational Mathematics
  • Applied Mathematics


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