Infinite-dimensional symmetries of two-dimensional coset models
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It has long been appreciated that the toroidal reduction of any gravity or supergravity to two dimensions gives rise to a scalar coset theory exhibiting an infinite-dimensional global symmetry. This symmetry is an extension of the finite-dimensional symmetry G in three dimensions, after performing a further circle reduction. There has not been universal agreement as to exactly what the extended symmetry algebra is, with different arguments seemingly concluding either that it is over(G, ), the affine Kac-Moody extension of G, or else a subalgebra thereof. We take the very explicit approach of Schwarz as our starting point for studying the simpler situation of two-dimensional flat-space sigma models, which nonetheless capture all the essential details. We arrive at the conclusion that the full symmetry is described by the Kac-Moody algebra over(G, ), whilst the subalgebra obtained by Schwarz arises as a gauge-fixed truncation. We then consider the explicit example of the SL (2, R) / O (2) coset, and relate Schwarz's approach to an earlier discussion that goes back to the work of Geroch. 2008 Elsevier B.V. All rights reserved.