Dr Daniele Dorigoni daniele.dorigoni@durham.ac.uk
Associate Professor
Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D N=2 field theories
Dorigoni, Daniele; Glass, Philip
Authors
Philip Glass
Abstract
We study three dimensional N = 2 supersymmetric abelian gauge theories with various matter contents living on a squashed sphere. In particular we focus on two problems: firstly we perform a Picard-Lefschetz decomposition of the localised path integral but, due to the absence of a topological theta angle in three dimensions, we find that steepest descent cycles do not permit us to distinguish between contributions to the path- integral coming from (would-be) different topological sectors, for example a vortex from a vortex/anti-vortex. The second problem we analyse is the truncation of all perturbative expansions. Although the partition function can be written as a transseries expansion of perturbative plus non-perturbative terms, due to the supersymmetric nature of the observable studied we have that each perturbative expansion around trivial and non-trivial saddles truncates suggesting that normal resurgence analysis cannot be directly applied. The first problem is solved by complexifying the squashing parameter, which can be thought of as introducing a chemical potential for the global U(1) rotation symmetry, or equivalently an omega deformation. This effectively introduces a hidden “topological angle” into the theory and the path integral can be now decomposed into a sum over different topological sectors via Picard-Lefschetz theory. The second problem is solved by deforming the matter content making manifest the Cheshire Cat resurgence structure of the supersymmetric theory, allowing us to reconstruct non-perturbative information from perturbative data even when these do truncate.
Citation
Dorigoni, D., & Glass, P. (2019). Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D N=2 field theories. Journal of High Energy Physics, 2019(12), Article 85. https://doi.org/10.1007/jhep12%282019%29085
Journal Article Type | Article |
---|---|
Acceptance Date | Nov 23, 2019 |
Online Publication Date | Dec 10, 2019 |
Publication Date | Dec 10, 2019 |
Deposit Date | Oct 2, 2019 |
Publicly Available Date | Jan 8, 2020 |
Journal | Journal of High Energy Physics |
Print ISSN | 1126-6708 |
Electronic ISSN | 1029-8479 |
Publisher | Scuola Internazionale Superiore di Studi Avanzati (SISSA) |
Peer Reviewed | Peer Reviewed |
Volume | 2019 |
Issue | 12 |
Article Number | 85 |
DOI | https://doi.org/10.1007/jhep12%282019%29085 |
Public URL | https://durham-repository.worktribe.com/output/1290095 |
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Copyright Statement
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any medium, provided the original author(s) and source are credite
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