Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-11-17
Adv.Theor.Math.Phys. 8 (2005) 895-937
Physics
High Energy Physics
High Energy Physics - Theory
analysis of sect. 5 generalized; 43 pages, Plain TeX, no figures, requires AMS font files amssym.def and amssym.tex
Scientific paper
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.
No associations
LandOfFree
Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-605373