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Gluing II: boundary localization and gluing formulas

Dedushenko, Mykola (2021) Gluing II: boundary localization and gluing formulas. Letters in Mathematical Physics, 111 (1). Art. No. 18. ISSN 0377-9017. doi:10.1007/s11005-021-01355-8.

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We describe applications of the gluing formalism discussed in the companion paper. When a d-dimensional local theory QFT_d is supersymmetric, and if we can find a supersymmetric polarization for QFT_d quantized on a (d−1)-manifold W, gluing along W is described by a non-local QFT_(d−1) that has an induced supersymmetry. Applying supersymmetric localization to QFT_(d−1), which we refer to as the boundary localization, allows in some cases to represent gluing by finite-dimensional integrals over appropriate spaces of supersymmetric boundary conditions. We follow this strategy to derive a number of “gluing formulas” in various dimensions, some of which are new and some of which have been previously conjectured. First we show how gluing in supersymmetric quantum mechanics can reduce to a sum over a finite set of boundary conditions. Then we derive two gluing formulas for 3D N=4 theories on spheres: one providing the Coulomb branch representation of gluing and another providing the Higgs branch representation. This allows to study various properties of their (2, 2)-preserving boundary conditions in relation to mirror symmetry. After that we derive a gluing formula in 4D N=2 theories on spheres, both squashed and round. First we apply it to predict the hemisphere partition function, then we apply it to the study of boundary conditions and domain walls in these theories. Finally, we mention how to glue half-indices of 4D N=2 theories.

Item Type:Article
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Dedushenko, Mykola0000-0002-9273-7602
Additional Information:© The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2021. Received: 25 January 2020; Revised: 25 January 2020; Accepted: 21 January 2021. This work was supported by the Walter Burke Institute for Theoretical Physics and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, as well as the Sherman Fairchild Foundation. The author thanks Tudor Dimofte, Yale Fan, Bruno Le Floch, Davide Gaiotto, Sergei Gukov, Victor Mikhaylov, Alexei Morozov, Natalie Paquette, Silviu Pufu, Mauricio Romo, David Simmons-Duffin, Gustavo J. Turiaci, Ran Yacoby for comments and discussions, and in particular Tudor Dimofte and Sergei Gukov for comments on the draft. The author declares that he has no conflict of interest.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Sherman Fairchild FoundationUNSPECIFIED
Subject Keywords:Gluing law; Supersymmetric localization; Local quantum field theory; Segal’s axioms
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Other Numbering System NameOther Numbering System ID
Issue or Number:1
Classification Code:MSC: 81T60; 81S40; 81T20; 81S10
Record Number:CaltechAUTHORS:20180716-140054929
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Official Citation:Dedushenko, M. Gluing II: boundary localization and gluing formulas. Lett Math Phys 111, 18 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87892
Deposited By: Joy Painter
Deposited On:16 Jul 2018 22:59
Last Modified:16 Nov 2021 00:21

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