A BRST analysis of W-symmetries

Abstract

We perform a classical BRST analysis of the symmetries corresponding to a generic w N -algebra. An essential feature of our method is that we write the w N -algebra in a special basis such that the algebra manifestly has a "nested" set of subalgebras v N N ⊂ v N −1

Spinor field realizations of non-critical strings

“…Such W 3 string is a theory of W 3 matter coupled to W 3 gravity; it is a generalization of two-dimensional matter couple to gravity. Shortly, a non-critical BRST charge for the W 2,4 string was constructed by generalizing the W 3 results of [16][17][18]. And some of the physical states, including some of the ghost-number zero ground-ring generators, were obtained.…”

“…where f 4 [6], f 4 [7], f 4 [8], f 4 [10], f 4 [14], f 4 [15], f 4 [18], f 4 [20] are arbitrary constants but do not vanish at the same time.…”

D = 11 Supermembrane instantons,W∞ strings and the super Toda molecule

“…The role of the unitary Virasoro minimal models in the expression for the central charge given by (14) was explained and clarified by [29] when they constructed in general the BRST operator corresponding to a W N algebra as a nested sum of nilpotent and mutually anticommuting BRST operators. This required a new basis in the Hilbert space.…”

“…In the noncritical W N string case [29] the matter and Liouville sector of the W N algebra can be realized in terms of N − 1 scalars, φ k ; σ k , respectively. These realizations in general have background charges which are fixed by the Miura transformations [29,36].…”

“…Since the Liouville modes are present then c m + c L + c g = 0 ⇒ c m = −2. Furthermore, the vast literature on Quantum Groups should provide insights as to how quantize the membrane : the Quantum Liouville theory has been extensively studied from many points of view ; mainly in the continuum limit, matrix models .... [29]. The group to be studied is :…”