Martin Cederwall: Extended geometry: superalgebras and cohomological formulation

Abstract

 Gravity and theories containing gravity (e.g. supergravity) exhibit (local) “hidden” symmetries. This becomes particularly interesting when it comes to symmetries manifested in a 2+(d-2) or 1+(d-1) split, by extending “internal” (d-2)-vectors to a module of an affine Kac-Moody algebra, or (d-1)-vectors to a module of an over-extended (typically hyperbolic) Kac-Moody algebra. The framework is extended geometry. I will sketch how the field content (in the BV sense) is obtained from level decompositions of certain superalgebras, and how the brackets on vector fields (and more) are obtained as derived brackets. I will also describe the BV complex and how to obtain dynamics. The talk builds mainly on joint work with Jakob Palmkvist.