Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory
| dc.creator | Zucchini, Roberto | |
| dc.date | 2003-11-17 | |
| dc.date | 2004-01-22 | |
| dc.date.accessioned | 2026-07-07T06:20:26Z | |
| dc.date.available | 2026-07-07T06:20:26Z | |
| dc.description | 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. | |
| dc.description | analysis of sect. 5 generalized; 43 pages, Plain TeX, no figures, requires AMS font files amssym.def and amssym.tex | |
| dc.identifier | https://arxiv.org/abs/hep-th/0311143 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0311143 | |
| dc.identifier | Adv.Theor.Math.Phys. 8 (2005) 895-937 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95325 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory | |
| dc.type | text |