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Reviving 3D \( \mathcal{N} \) = 8 superconformal field theories

  • Olaf HohmEmail author
  • Henning Samtleben
Open Access
Regular Article - Theoretical Physics
  • 31 Downloads

Abstract

We present a Lagrangian formulation for \( \mathcal{N} \) = 8 superconformal field theories in three spacetime dimensions that is general enough to encompass infinite-dimensional gauge algebras that generally go beyond Lie algebras. To this end we employ Chern-Simons theories based on Leibniz algebras, which give rise to L algebras and are defined on the dual space \( \mathfrak{g} \)* of a Lie algebra \( \mathfrak{g} \) by means of an embedding tensor map ϑ: \( \mathfrak{g} \)*\( \mathfrak{g} \). We show that for the Lie algebra \( \mathfrak{sdif}{\mathfrak{f}}_3 \) of volume-preserving diffeomorphisms on a 3-manifold there is a natural embedding tensor defining a Leibniz algebra on the space of one-forms. Specifically, we show that the cotangent bundle to any 3-manifold with a volume-form carries the structure of a (generalized) Courant algebroid. The resulting \( \mathcal{N} \) = 8 superconformal field theories are shown to be equivalent to Bandos-Townsend theories. We show that the theory based on S3 is an infinite-dimensional generalization of the Bagger-Lambert-Gustavsson model that in turn is a consistent truncation of the full theory. We also review a Scherk-Schwarz reduction on S2 × S1, which gives the super-Yang-Mills theory with gauge algebra \( \mathfrak{sdif}{\mathfrak{f}}_2 \), and we construct massive deformations.

Keywords

Chern-Simons Theories Conformal Field Models in String Theory Extended Supersymmetry M-Theory 

Notes

Open Access

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

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute for PhysicsHumboldt University BerlinBerlinGermany
  2. 2.Simons Center for Geometry and PhysicsStony Brook UniversityStony BrookU.S.A.
  3. 3.Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de PhysiqueLyonFrance

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