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October, 2004 Four Dimensional Abelian Duality and DL (2,Z) Action in Three Dimensional Conformal Field Theory
Roberto Zucchini
Adv. Theor. Math. Phys. 8(5): 895-936 (October, 2004).


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 = S3. We further identify a class of homology 3–spheres N for which Witten's conjecture takes a particular simple form.


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Roberto Zucchini. "Four Dimensional Abelian Duality and DL (2,Z) Action in Three Dimensional Conformal Field Theory." Adv. Theor. Math. Phys. 8 (5) 895 - 936, October, 2004.


Published: October, 2004
First available in Project Euclid: 2 June 2005

zbMATH: 1097.81048
MathSciNet: MR2160774

Rights: Copyright © 2004 International Press of Boston


Vol.8 • No. 5 • October, 2004
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