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arXiv · 1504.06555

Higher Spin Lifshitz Theories and the KdV-Hierarchy

Matteo Beccaria·Michael Gutperle·Yi Li·Guido Macorini
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Abstract

In this paper three dimensional higher spin theories in the Chern-Simons formulation with gauge algebra $sl(N,R)$ are investigated which have Lifshitz symmetry with scaling exponent $z$. We show that an explicit map exists for all $z$ and $N$ relating the Lifshitz Chern-Simons theory to the $(n,m)$ element of the KdV hierarchy. Furthermore we show that the map and hence the conserved charges are independent of $z$. We derive these result from the Drinfeld-Sokolov formalism of integrable systems.

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Matteo Beccaria, Michael Gutperle, Yi Li, Guido Macorini. 2015-04-24. Higher Spin Lifshitz Theories and the KdV-Hierarchy. https://doi.org/10.1103/physrevd.92.085005

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