Recently, Witten showed that there is a natural action of the group SL(2,Z)
on the space of 3 dimensional conformal field theories with U(1) global
symmetry and a chosen coupling of the symmetry current to a background gauge
field on a 3-fold N. He further argued that, for a class of conformal field
theories, in the nearly Gaussian limit, this SL(2,Z) action may be viewed as a
holographic image of the well-known SL(2,Z) Abelian duality of a pure U(1)
gauge theory on AdS-like 4-folds M bounded by N, as dictated by the AdS/CFT
correspondence. However, he showed that explicitly only for the generator T;
for the generator S, instead, his analysis remained conjectural. In this paper,
we propose a solution of this problem. We derive a general holographic formula
for the nearly Gaussian generating functional of the correlators of the
symmetry current and, using this, we show that Witten's conjecture is indeed
correct when N=S^3. We further identify a class of homology 3-spheres N for
which Witten's conjecture takes a particular simple form.Comment: analysis of sect. 5 generalized; 43 pages, Plain TeX, no figures,
requires AMS font files amssym.def and amssym.te
