Kac-Moody and Virasoro symmetries of principal chiral sigma models
Additional Document Info
It is commonly asserted that there is a over(G, ) G centreless Kac-Moody extension of the manifest G G global symmetry of the two-dimensional principal chiral model (PCM) for the group manifold G. Here, we show that the symmetry is in fact larger, namely over(G, ) over(G, ), the full centreless Kac-Moody extension of the entire manifest G G global symmetry. Extending previous results in the literature, we also obtain an explicit realisation of the Virasoro-like symmetry of the PCM, generated by Kn = Ln + 1 - Ln - 1 for both positive and negative n. We show that these generators obey Sugawara-type commutation relations with the two commuting copies of the Kac-Moody algebra over(G, ). 2009 Elsevier B.V. All rights reserved.