Kac–Moody and Virasoro symmetries of principal chiral sigma models Original Research Article

It is commonly asserted that there is a image centreless Kac–Moody extension of the manifest image 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 image, the full centreless Kac–Moody extension of the entire manifest image global symmetry. Extending previous results in the literature, we also obtain an explicit realisation of the Virasoro-like symmetry of the PCM, generated by image 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 image.