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Fivebranes and 4-Manifolds

Gadde, Abhijit and Gukov, Sergei and Putrov, Pavel (2016) Fivebranes and 4-Manifolds. In: Arbeitstagung Bonn 2013. Progress in Mathematics. No.319. Springer , New York, NY, pp. 155-245. ISBN 978-3-319-43646-3.

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We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2)N=(0,2) theories, we obtain a number of results, which include new 3d N=2N=2 theories T[M 3] associated with rational homology spheres and new results for Vafa–Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0, 2) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines/walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d N=(0,2)N=(0,2) theories and 3d N=2N=2 theories, respectively.

Item Type:Book Section
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Gukov, Sergei0000-0002-9486-1762
Additional Information:© 2016 Springer International Publishing Switzerland. We thank F. Quinn, D. Roggenkamp, C. Schweigert, A. Stipsicz, and P. Teichner for patient and extremely helpful explanations.We also thank T. Dimofte, Y. Eliashberg, A. Kapustin, T. Mrowka, W. Neumann, T. Okazaki, E. Sharpe, C. Vafa, J. Walcher, and E. Witten, among others, for a wide variety of helpful comments. The work of A.G. is supported in part by the John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The work of P.P. is supported in part by the Sherman Fairchild scholarship and by NSF Grant PHY-1050729. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-92-ER40701
Department of Energy (DOE)DE-FG03-92-ER40701FG-02
Sherman Fairchild FoundationUNSPECIFIED
John A. McCone Postdoctoral FellowshipUNSPECIFIED
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Series Name:Progress in Mathematics
Issue or Number:319
Record Number:CaltechAUTHORS:20170615-083539862
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78238
Deposited By: Ruth Sustaita
Deposited On:15 Jun 2017 16:40
Last Modified:15 Nov 2021 17:37

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