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Title: Integration over the u-plane in Donaldson theory with surface operators
Authors: Tan, M.-C. 
Keywords: Differential and algebraic geometry
Duality in gauge field theories
Supersymmetric gauge theory
Topological field theories
Issue Date: 2011
Citation: Tan, M.-C. (2011). Integration over the u-plane in Donaldson theory with surface operators. Journal of High Energy Physics 2011 (5) : -. ScholarBank@NUS Repository.
Abstract: We generalize the analysis by Moore and Witten in [hep-th/9709193], and consider integration over the u-plane in Donaldson theory with surface operators on a smooth four-manifold X. Several novel aspects will be developed in the process; like a physical interpretation of the "ramified" Donaldson and Seiberg-Witten invariants, and the concept of curved surface operators which are necessarily topological at the outset. Elegant physical proofs | rooted in R-anomaly cancellations and modular invariance over the u- plane | of various seminal results in four-dimensional geometric topology obtained by Kronheimer-Mrowka [1, 2] | such as a universal formula relating the "ramified" and ordinary Donaldson invariants, and a generalization of the celebrated Thom conjecture | will be furnished. Wall-crossing and blow-up formulas of these "ramified" invariants which have not been computed in the mathematical literature before, as well as a generalization and a Seiberg-Witten analog of the universal formula as implied by an electric-magnetic duality of trivially-embedded surface operators in X, will also be presented, among other things. © SISSA 2011.
Source Title: Journal of High Energy Physics
ISSN: 11266708
DOI: 10.1007/JHEP05(2011)007
Appears in Collections:Staff Publications

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