Conformal internal symmetry of 2d σ-models 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 Kac-Moody algebra A1(1) and half of a real Witt algebra. In this paper we exhibit the full symmetry under the semi-direct 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 self-duality constraint that is the analog of the self-duality constraint arising in extended supergravities in higher space-time 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 non-linear σ-models 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 off-shell fields (in a fixed gauge) and preserves the equations of motion.
- Publication:
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Nuclear Physics B
- Pub Date:
- February 1996
- DOI:
- 10.1016/S0550-3213(96)00551-2
- arXiv:
- arXiv:hep-th/9608082
- Bibcode:
- 1996NuPhB.482..431J
- Keywords:
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- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 44 pages, LATEX