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Integration over the u-plane in Donaldson theory with surface operators

Tan, Meng-Chwan (2011) Integration over the u-plane in Donaldson theory with surface operators. Journal of High Energy Physics, 2011 (5). Art. No. 007. ISSN 1126-6708. https://resolver.caltech.edu/CaltechAUTHORS:20110718-103734529

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/JHEP05(2011)007DOIUNSPECIFIED
http://www.springerlink.com/content/f611k60h811j0268/PublisherUNSPECIFIED
http://arxiv.org/abs/0912.4261arXivUNSPECIFIED
Additional Information:© 2011 SISSA. Received: March 7, 2011. Accepted: April 21, 2011. Published: May 2, 2011. I would like to thank S. Gukov, G. Moore, N. Seiberg, P. Sulkowski, K. Vyas and especially C. LeBrun and T.S. Mrowka, for illuminating exchanges. This work is supported by the California Institute of Technology and the NUS-Overseas Postdoctoral Fellowship.
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Funding AgencyGrant Number
CaltechUNSPECIFIED
NUS-Overseas Postdoctoral Fellowship UNSPECIFIED
Subject Keywords:Supersymmetric gauge theory – Duality in Gauge Field Theories – Differential and Algebraic Geometry – Topological Field Theories
Issue or Number:5
Record Number:CaltechAUTHORS:20110718-103734529
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110718-103734529
Official Citation:Integration over the u-plane in Donaldson theory with surface operators Meng-Chwan Tan
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24445
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:18 Jul 2011 17:56
Last Modified:03 Oct 2019 02:56

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