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The u-plane integral is the contribution of the Coulomb branch to correlation functions of N=2 gauge theory on a compact four-manifold.
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D. Zagier, Ramanujan’s mock theta functions and their applications (after Zwegers and Ono-Bringmann) , Astérisque (2009) Exp. No. 986, vii–viii, 143–164 (2010)
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1996
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G. W. Moore and E. Witten, Integration over the u plane in Donaldson theory , Adv. Theor. Math. Phys. 1
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2012
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J. A. Harvey, “Permutation groups, Mock modular forms, K3 surfaces and Moonshine, Lectures at Isaac Newton Institute.” https://www.newton.ac.uk/seminar/20120126140015001 , 2012
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J. A. Harvey, “(Mock) Modular Forms and Applications to String Theory, Lectures at LACES, GGI.” https://www.youtube.com/watch?v=CSmKdMc3a64 , 2015
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S. Kachru, Elementary introduction to Moonshine , 2016 · 2016
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J. A. Harvey, “Moonshine and String Theory, Lectures at ICTP Spring School on Superstring Theory and Related Topics.” https://www.youtube.com/watch?v=NPI6bAI_Rdc , 2016
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G. Korpas and J. Manschot, Donaldson-Witten theory and indefinite theta functions , JHEP 11
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G. W. Moore, Lectures On The Physical Approach To Donaldson And Seiberg-Witten Invariants , Item 78 at http://www.physics.rutgers.edu/ gmoore/ (2017)
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V. Anagiannis and M. C. N. Cheng, TASI Lectures on Moonshine , PoS TASI2017
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