Preprint / Particle Physics - Theory hep-th/0307041

SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry

Witten, Edward (Princeton University)

2003

Abstract: On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group SL(2,Z). The generator S of SL(2,Z) acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler. The other generator T acts by shifting the Chern-Simons coupling of the background field. This SL(2,Z) action in three dimensions is related by the AdS/CFT correspondence to SL(2,Z) duality of low energy U(1) gauge fields in four dimensions.

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