On affine Lie superalgebras, AdS(3)/CFT correspondence and world-sheets for world-sheets

Space-time N = 2 and N = 4 superconformal algebras can be built using world -sheet free fields or, equivalently, free field representations of o (s) ov er cap p(1\2) and (s) over cap l(2\1), respectively, A prescription for the calculation of space-time correlators is given. As applications we compute one- and two-point correlation functions of Virasoro (superVirasoro) gener ators. We also present a possible scenario for taking into account of NS fi vebranes in the framework of our construction for the description of supers trings on AdS(3). It is nothing but a simplified version of Green's "world- sheets for world-sheets". (C) 1999 Elsevier Science B.V. All rights reserve d.