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Reviving 3D N=8{\cal N}=8 superconformal field theories

Oct 29, 2018
33 pages
Published in:
  • JHEP 04 (2019) 047
  • Published: Apr 4, 2019
e-Print:
DOI:
Report number:
  • HU-EP-18/31
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Abstract: (Springer)
We present a Lagrangian formulation for N \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 g∗ \mathfrak{g}^{*} of a Lie algebra g \mathfrak{g} by means of an embedding tensor map ϑ: g∗ \mathfrak{g}^{*} → g \mathfrak{g} . We show that for the Lie algebra sdiff3 \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 N \mathcal{N} = 8 superconformal field theories are shown to be equivalent to Bandos-Townsend theories. We show that the theory based on S3^{3} 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^{2} × S1^{1}, which gives the super-Yang-Mills theory with gauge algebra sdiff2 \mathfrak{sdif}{\mathfrak{f}}_2 , and we construct massive deformations.
Note:
  • 32 pages, v2: minor changes, version to appear in JHEP
  • Chern-Simons Theories
  • Conformal Field Models in String Theory
  • Extended Supersymmetry
  • M-Theory
  • algebra: Lie
  • field theory: conformal
  • algebra: gauge
  • tensor: embedding
  • space-time: dimension: 3
  • Bagger-Lambert-Gustavsson model
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