Kac-Moody and Virasoro Symmetries of Principal Chiral Sigma Models

Details Kac-Moody and Virasoro Symmetries of Principal Chiral Sigma Models Kac-Moody and Virasoro Symmetries of Principal Chiral Sigma Models

2008-12-11

arxiv.org/abs/0812.2218v2

Nucl.Phys.B826:71-86,2010

Physics

High Energy Physics

High Energy Physics - Theory

Reference added; discussion of earlier work extended

Scientific paper

10.1016/j.nuclphysb.2009.09.030

It is commonly asserted that there is a \hat G\times G centreless Kac-Moody extension of the manifest G\times 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 \hat G\times \hat G, the full centreless Kac-Moody extension of the entire manifest G\times 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 K_n=L_{n+1} - L_{n-1} for both positive and negative n. We show that these generators obey Sugarawara-type commutation relations with the two commuting copies of the Kac-Moody algebra \hat G.

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