UCLA

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 Korteweg-de Vries 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.