General Two-Dimensional Supergravity from Poisson Superalgebras

Details General Two-Dimensional Supergravity from Poisson Superalgebras General Two-Dimensional Supergravity from Poisson Superalgebras

2000-12-21

arxiv.org/abs/hep-th/0012219v1

JHEP 0101:042,2001

Physics

High Energy Physics

High Energy Physics - Theory

70 pages, LaTeX, AMSmath, BibTeX

Scientific paper

10.1088/1126-6708/2001/01/042

We provide the geometric actions for most general N=1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N. This provides a supersymmetrization of any generalized dilaton gravity theory or of any theory with an action being an (essentially) arbitrary function of curvature and torsion. Technically we proceed as follows: The bosonic part of any of these theories may be characterized by a generically nonlinear Poisson bracket on a three-dimensional target space. In analogy to a given ordinary Lie algebra, we derive all possible N=1 extensions of any of the given Poisson (or W-) algebras. Using the concept of graded Poisson Sigma Models, any extension of the algebra yields a possible supergravity extension of the original theory, local Lorentz and super-diffeomorphism invariance follow by construction. Our procedure automatically restricts the fermionic extension to the minimal one; thus local supersymmetry is realized on-shell. By avoiding a superfield approach we are also able to circumvent in this way the introduction of constraints and their solution. For many well-known dilaton theories different supergravity extensions are derived. In generic cases their field equations are solved explicitly.

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