Electric-Magnetic Duality and Deformations of Three-Dimensional Conformal Field Theories

SL(2,Z) duality transformations in asymptotically AdS4 x S7 act nontrivially on the three-dimensional superconformal field theory of coincident M2-branes on the boundary. We show how S-duality acts away from the IR fixed point.We develop a systematic method to holographically obtain the deformations of the boundary CFT and show how electric-magnetic duality relates different deformations. We analyze in detail marginal deformations and deformations by dimension 4 operators. In the case of massive deformations, the renormalization group flow relates S-dual CFT’s. Correlation functions in the CFT are computed by varying magnetic bulk sources, whereas correlation functions in the dual CFT are computed by electric bulk sources. Under massive deformations, the boundary effective action is generically minimized by massive self-dual configurations of the U(1) gauge field. We show that a self-dual choice of boundary conditions exists, and it corresponds to the self-dual topologically massive gauge theory in 2 + 1 dimensions. Thus, self-duality in three dimensions can be understood as a consequence of electric-magnetic invariance in the bulk of AdS4. Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: de Haro, S. and Gao, P. (2007). Electric-magnetic duality and deformations of three-dimensional conformal field theories. Physical Review D. 76, 106008. © 2007 The American Physical Society http://dx.doi.org/10.1003/PhysRevD.76.106008 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/125 Electric-magnetic duality and deformations of three-dimensional conformal field theories Sebastian de Haro and Peng Gao Department of Mathematics, King’s College, London WC2R 2LS, United Kingdom Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA (Received 19 July 2007; published 12 November 2007) SL 2;Z duality transformations in asymptotically AdS4 S7 act nontrivially on the three-dimensional superconformal field theory of coincident M2-branes on the boundary. We show how S-duality acts away from the IR fixed point. We develop a systematic method to holographically obtain the deformations of the boundary CFT and show how electric-magnetic duality relates different deformations. We analyze in detail marginal deformations and deformations by dimension 4 operators. In the case of massive deformations, the renormalization group flow relates S-dual CFT’s. Correlation functions in the CFT are computed by varying magnetic bulk sources, whereas correlation functions in the dual CFT are computed by electric bulk sources. Under massive deformations, the boundary effective action is generically minimized by massive self-dual configurations of the U 1 gauge field. We show that a self-dual choice of boundary conditions exists, and it corresponds to the self-dual topologically massive gauge theory in 2 1 dimensions. Thus, self-duality in three dimensions can be understood as a consequence of electric-magnetic invariance in the bulk of AdS4. DOI: 10.1103/PhysRevD.76.106008 PACS numbers: 11.25.Tq