Physics Group Meeting

We review some infinite dimensional symmetries that appear in dimensionally reduced classical general relativity. Reducing from d=4 to d=2 gives a two dimensional nonlinear sigma model with an infinite dimensional affine Kac-Moody symmetry called the Geroch group. Further reducing to d=1 (along a null Kill vector) enhances the Geroch group to a mysterious "hyperbolic Kac-Moody" symmetry.Further reading:
[1] P. Breitenlohner and D. Maison, "On the Geroch group," Ann. Inst. H. Poincare, 46, 215 (1987)
[2] H. Nicolai, "Two-dimensional gravities and supergravities as integrable systems," in “Schladming 1991, Proceedings, Recent aspects of quantum fields,” 231, and Hamburg DESY 91-038
[3] H. Lu, M. Perry, and C. Pope, ArXiv:0711.0400 and ArXiv:0712.0615