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Mocking the u-plane integral

Journal Article · · Research in the Mathematical Sciences (Print)
; ; ;

Abstract

Theu-plane integral is the contribution of the Coulomb branch to correlation functions of$$$${\mathcal {N}}=2$$$$ N = 2 gauge theory on a compact four-manifold. We consider theu-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group$$$$\mathrm{SU}(2)$$$$ SU ( 2 ) , for an arbitrary four-manifold with$$$$(b_1,b_2^+)=(0,1)$$$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . Theu-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 theu-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.

Research Organization:
Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0010008
OSTI ID:
1851275
Journal Information:
Research in the Mathematical Sciences (Print), Vol. 8, Issue 3; ISSN 2522-0144
Publisher:
SpringerOpen
Country of Publication:
United States
Language:
English

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