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Gluing II: Boundary Localization and Gluing Formulas

Dedushenko, Mykola (2018) Gluing II: Boundary Localization and Gluing Formulas. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20180716-140054929

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Abstract

We describe applications of the gluing formalism discussed in the companion paper. When a d-dimensional local theory QFTd is supersymmetric, and if we can find a supersymmetric polarization for QFTd quantized on a (d − 1)-manifold W, gluing along W is described by a non-local QFTd−1 that has an induced supersymmetry. Applying supersymmetric localization to QFTd−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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1807.04278arXivDiscussion Paper
Additional Information: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. 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.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Sherman Fairchild FoundationUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2018-025
Record Number:CaltechAUTHORS:20180716-140054929
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180716-140054929
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87892
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:16 Jul 2018 22:59
Last Modified:16 Jul 2018 22:59

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