Classical Solutions for Poisson Sigma Models on a Riemann surface

Abstract

We determine the moduli space of classical solutions to the field equations of Poisson Sigma Models on arbitrary Riemann surfaces for Poisson structures with vanishing Poisson form class. This condition ensures the existence of a presymplectic form on the target Poisson manifold which agrees with the induced symplectic forms of the Poisson tensor upon pullback to the leaves. The dimension of the classical moduli space as a function of the genus of the worldsheet Sigma and the corank k of the Poisson tensor is determined as k(rank(H^1(Sigma))+1). Representatives of the classical solutions are provided using the above mentioned presymplectic 2-forms, and possible generalizations to cases where such a form does not exist are discussed. The results are compared to the known moduli space of classical solutions for two-dimensional BF and Yang-Mills theories.

arXiv comment28 pages

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• Strings in Singular Space-Times and their Universal Gauge Theory
• Equivalences between 2D dilaton gravities, their asymptotic symmetries, and their holographic duals