Published June 11, 2009
| Version Submitted
Journal Article
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The algebra of Wilson–'t Hooft operators
Abstract
We study the Operator Product Expansion of Wilson–'t Hooft operators in a twisted N=4 super-Yang–Mills theory with gauge group G. The Montonen–Olive duality puts strong constraints on the OPE and in the case G=SU(2) completely determines it. From the mathematical point of view, the Montonen–Olive duality predicts the L^2 Dolbeault cohomology of certain equivariant vector bundles on Schubert cells in the affine Grassmannian. We verify some of these predictions. We also make some general observations about higher categories and defects in Topological Field Theories.
Additional Information
© 2009 Elsevier B.V. Received 26 November 2008; accepted 3 February 2009 Available online 10 February 2009. We would like to thank R. Bezrukavnikov, A. Braverman, S. Gukov, M. Finkelberg, I. Mirkovic, L. Positselski and E. Witten for discussions. We are especially grateful to R. Bezrukavnikov for valuable advice without which this work would not be possible.We would like to express our thanks to the Aspen Center for Physics for hospitality. A.K. is also grateful to the Independent University of Moscow for staying open during the winter holidays of 2006–2007 and thereby providing an opportunity to share some preliminary results with interested mathematicians and to receive their feedback. This work was supported in part by the DOE grant DE-FG03-92-ER40701.Attached Files
Submitted - 0710.2097v1.pdf
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0710.2097v1.pdf
Additional details
Identifiers
- Eprint ID
- 14424
- Resolver ID
- CaltechAUTHORS:20090623-092906678
Related works
- Describes
- http://arxiv.org/abs/0710.2097 (URL)
Funding
- Department of Energy (DOE)
- DE-FG03-92-ER40701
Dates
- Created
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2009-08-13Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field
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- Mathematics Department