1998/10/27 by Matthew J. Strassler, Strassler, Matthew J.
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9810223
arxiv created 1998/10/27 · arxiv updated 2009/11/30
As in two and four dimensions, supersymmetric conformal field theories in three dimensions can have exactly marginal operators. These are illustrated in a number of examples with N=4 and N=2 supersymmetry. The N=2 theory of three chiral multiplets X,Y,Z and superpotential W=XYZ has an exactly marginal operator; N=2 U(1) with one electron, which is mirror to this theory, has one also. Many N=4 fixed points with superpotentials W ∼ Phi Qi Qi have exactly marginal deformations consisting of a combination of Phi2 and (Qi Qi)2. However, N=4 U(1) with one electron does not; in fact the operator Phi2 is marginally irrelevant. The situation in non-abelian theories is similar. The relation of the marginal operators to brane rotations is briefly discussed; this is particularly simple for self-dual examples where the precise form of the marginal operator may be guessed using mirror symmetry.