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Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D N=2 field theories

Dorigoni, Daniele; Glass, Philip

Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D N=2 field theories Thumbnail


Philip Glass


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.


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.

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
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2019
Issue 12
Article Number 85


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This article is distributed under the terms of the Creative Commons<br /> Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in<br /> any medium, provided the original author(s) and source are credite

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