New Linear Systems for 2D Poincare Supergravities

Details New Linear Systems for 2D Poincare Supergravities New Linear Systems for 2D Poincare Supergravities

1993-09-09

arxiv.org/abs/hep-th/9309052v1

Nucl.Phys. B414 (1994) 299-328

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, report DESY93-122

Scientific paper

10.1016/0550-3213(94)90432-4

A new linear system is constructed for Poincar\'e supergravities in two dimensions. In contrast to previous results, which were based on the conformal gauge, this linear system involves the topological world sheet degrees of freedom (the Beltrami and super-Beltrami differentials). The associated spectral parameter likewise depends on these and is itself subject to a pair of differential equations, whose integrability condition yields one of the equations of motion. These results suggest the existence of an extension of the Geroch group mixing propagating and topological degrees of freedom on the world sheet. We also develop a chiral tensor formalism for arbitrary Beltrami differentials, in which the factorization of $2d$ diffeomorphisms is always manifest.

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