Higher-spin Gauge Interactions for Matter Fields in Two Dimensions

Many of important properties of integrable systems and conformal models in two dimensions originate from underlying infinite-dimensional symmetries. Higher-spin (HS) extensions of the Virasoro symmetry acquired much attention during recent years. In particular, d2 conformal matter models with gauged HS symmetries have been extensively studied for the cases of WN [1], ω∞ [2] and W1+∞ [3, 4] algebras. A d=2 model for pure gauge W1+∞ HS fields was proposed in [5]. The W1+∞ algebra investigated originally in [6] is getting now a wide area of applicability including, e.g., fractional Hall effect [7] and KP hierarchy [8]. In the context of field theory W1+∞ type symmetries were originally introduced as HS symmetries in [3] for the case of d=2, and in [10, 11] for d=4. The name W1+∞ was suggested in [12] in the context of the analysis of possible Lie algebra extensions of the Virasoro algebra. In refs. [13] and [14, 15] consistent dynamics of HS gauge fields interacting among themselves and with the lower-spin matter fields in d=4 and d=3 was formulated in terms of gauge fields corresponding to the appropriate versions of W1+∞-type algebras. An interesting problem that remained unsolved for some years was to apply the methods developed for d=3 and d=4 HS problems to d2 models. The goal of this letter is just to announce a new model which describes HS gauge interactions of boson and fermion matter fields in d=2 along the lines of the approach developed in [13-15]. As expected, the d2 HS dynamics turns out to be much simpler than that in d=3 and 4. However, the formalism in d=2 has a number of specific properties and does not amount to a straightforward