Generalized 2d dilaton gravity with matter fields

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Abstract
We extend the classical integrability of the CGHS model of 2d dilaton gravity [1] to a larger class of models, allowing the gravitational part of the action to depend more generally on the dilaton field and, simultaneously adding fermion and U(1) gauge fields to the scalar matter. On the other hand we provide the complete solution of the most general dilaton dependent 2d gravity action coupled to chiral fermions. The latter analysis is generalized to a chiral fermion multiplet with a non-abelian gauge symmetry as well as to the (anti-)self-dual sector df=+/-*df of a scalar field f.

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