SL(2, Z) ACTION ON THREE-DIMENSIONAL CONFORMAL FIELD THEORIES WITH ABELIAN SYMMETRY [chapter]

EDWARD WITTEN
2005 From Fields to Strings: Circumnavigating Theoretical Physics  
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 in explaining three-dimensional mirror symmetry. The other generator T acts by shifting the Chern-Simons coupling of the background field. This SL(2, Z) action in three
more » ... nsions is related by the AdS/CFT correspondence to SL(2, Z) duality of low energy U (1) gauge fields in four dimensions.
doi:10.1142/9789812775344_0028 fatcat:ryhfif42czgd5mv3oe5rzvkyqq