Low energy dynamics from deformed conformal symmetry in quantum 4D [formula omitted] SCFTs

Abstract

We determine the one-loop deformation of the conformal symmetry of a general N=2 superconformally invariant Yang–Mills theory. The deformation is computed for several explicit examples which have a realization as world-volume theories on a stack of D3 branes. These include: (i) N=4 SYM with gauge groups SU( N), USp(2 N) and SO( N); (ii) USp(2 N) gauge theory with one hypermultiplet in the traceless antisymmetric representation and four hypermultiplets in the fundamental; (iii) quiver gauge theory with gauge group SU( N)× SU( N) and two hypermultiplets in the bifundamental representations ( N , N ) and ( N , N ) . The existence of quantum corrections to the conformal transformations imposes restrictions on the effective action which we study on a subset of the Coulomb branch corresponding to the separation of one brane from the stack. In the N=4 case, the one-loop corrected transformations provide a realization of the conformal algebra; this deformation is shown to be one-loop exact. For the other two models, higher-loop corrections are necessary to close the algebra. Requiring closure, we infer the two-loop conformal deformation.