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A bstract Three-dimensional $$ \mathcal{N} $$ N = 4 superconformal field theories contain 1d topological sectors consisting of twisted linear combinations of half-BPS local operators that can be inserted anywhere along a line. After a conformal mapping to a round three-sphere, the 1d sectors are now defined on a great circle of S 3 . We show that the 1d topological sectors are preserved under the squashing of the sphere. For gauge theories with matter hypermultiplets, we use supersymmetric localization to derive an explicit description of the topological sector associated with the Higgs branch. Furthermore, we find that the dependence of the 1d correlation functions on the squashing parameter b can be removed after appropriate rescalings. One can introduce real mass and Fayet-Iliopolous parameters that, after appropriate rescalings, modify the 1d theory on the squashed sphere precisely as they do on the round sphere. In addition, we also show that when a generic 3d $$ \mathcal{N} $$ N = 4 theory is deformed by real mass parameters, this deformation translates into a universal deformation of the corresponding 1d theory.
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Framed 𝔼n-algebras from quantum field theory
This paper addresses the following question: given a topological quantum field theory on [Formula: see text] built from an action functional, when is it possible to globalize the theory so that it makes sense on an arbitrary smooth oriented n-manifold? We study a broad class of topological field theories — those of AKSZ type — and obtain an explicit condition for the vanishing of the framing anomaly, i.e. the obstruction to performing this globalization procedure. We also interpret our results in terms of identifying the observables as an algebra over the framed little n-disks operad. Our analysis uses the BV formalism for perturbative field theory and the notion of factorization homology.
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- Award ID(s):
- 2042052
- PAR ID:
- 10582221
- Publisher / Repository:
- World Scientific
- Date Published:
- Journal Name:
- Reviews in Mathematical Physics
- Volume:
- 35
- Issue:
- 07
- ISSN:
- 0129-055X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0129055X23500113
