N=2 W Supergravity

Abstract

We quantize the classical gauge theory of N = 2 Woo supergravity and show how the underlying N = 2 super-woo algebra gets deformed into an N = 2 super-Woo algebra. Both algebras contain the N = 2 super-Virasoro algebra as a subalgebra. We discuss how one can extract from these results information about quantum N = 2 WN supergravity theories containing a finite number of higher-spin symmetries with superspin s ≤ N. As an example we discuss the case of quantum N = 2 W3 supergravity.

Multi-field coset space realizations of w 1+ infinity

“…This fact has been noticed in ref. [8] where it has been also observed that, by adjusting the parameter value, one can cancel the central charge in the spin 1 sector of w 1+∞ and so make the modified currents obey the centreless w 1+∞ . As it is seen from the OPE's (3.3) and (3.14), in our notation this cancellation occurs at…”

“…4.1 and demonstrate that the two-field realizations of ref. [3,8] can be derived in this way. Secondly, one may still deal with the same w 1+∞ as in ref.…”

“…A closely related observation is that it naturally appears as the bosonic subsystem in the following N = 2 supersymmetric extension of the (1 + 1) action (3.6), (3.8): one can N = 2 supersymmetrize this action by introducing two N = 2 chiral superfields with the kinetic terms of the opposite sign. Then one may hope that the (2 + 2) system in question could be given a coset space interpretation in the framework of the nonlinear realizations of N = 2 super w 1+∞ algebras [15,8], along the lines of [1] and the present paper. Finally, we wish to point out that our three-field system action (5.1) coincides with the free part of the action for the conformal affine Toda (CAT) system [4], e.g.…”

Extended conformal symmetries

“…The OPE's where s and/or I equals 1/2 can be found in ref. [25]. By definition, the symbol s~2is equal to zero fors even and 1 for s odd.…”

“…Its generic expression is given by [24,t;~)(12)S+t+1/22(S+t)I, + regular part. (30)The structure functions J~(D1,D2A) are polynomials in the supercovariant derivatives of degree 2u -1, whose explicit form is given in ref [25]…”