Conformal internal symmetry of 2d σmodels coupled to gravity and a dilaton
Abstract
General relativity reduced to two dimensions possesses a large group of symmetries that exchange classical solutions. The associated Lie algebra is known to contain the affine KacMoody algebra A_{1}^{(1)} and half of a real Witt algebra. In this paper we exhibit the full symmetry under the semidirect product of Lie A( _{1}^{(1)}) by the Witt algebra Lie ( W), Furthermore we exhibit the corresponding hidden gauge symmetries. We show that the theory can be understood in terms of an infinite dimensional potential space involving all degrees of freedom: the dilaton as well as matter and gravitation. In the dilaton sector the linear system that extends the previously known Lax pair has the form of a twisted selfduality constraint that is the analog of the selfduality constraint arising in extended supergravities in higher spacetime dimensions. Our results furnish a group theoretical explanation for the simultaneous occurrence of two spectral parameters, a constant one (= y) and a variable one (= t). They hodl for all 2d nonlinear σmodels that are obtained by dimensional reduction of G/ H models in three dimensions coupled to pure gravity. In that case the Lie algebra is Lie ( W⋉ G ^{(1)}) ; this symmetry acts on a set of offshell fields (in a fixed gauge) and preserves the equations of motion.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1996
 DOI:
 10.1016/S05503213(96)005512
 arXiv:
 arXiv:hepth/9608082
 Bibcode:
 1996NuPhB.482..431J
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 44 pages, LATEX