Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry

Laurent Baulieu (1, 2) , Guillaume Bossard (1) , Alessandro Tanzini (3)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2 Department of Physics and Astronomy [Piscataway]
3 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies

The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincaré supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting "equivariant topological field theory" corresponds to the twist of super Yang-Mills theory on Omega backgrounds.

Mots clés: TQFT; supersymmetry; Yang-Mills

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Laurent Baulieu, Guillaume Bossard, Alessandro Tanzini. Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry. Journal of High Energy Physics, 2005, 508, pp.37. ⟨hal-00004808v3⟩