On Renormalization Group Flows and Exactly Marginal Operators in Three Dimensions

Abstract

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 \sim Phi Q_i \tilde Q^i have exactly marginal deformations consisting of a combination of Phi^2 and (Q_i \tilde Q^i)^2. However, N=4 U(1) with one electron does not; in fact the operator Phi^2 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.

References in corpus (6)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Mirror Symmetry in Three Dimensional Gauge Theories
• Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes
• Three Dimensional SCFT from M2 Branes at Conifold Singularities
• Manifolds of Fixed Points and Duality in Supersymmetric Gauge Theories

Cited by in corpus (7)

• Decoding a Three-Dimensional Conformal Manifold
• D-Brane Probes of Special Holonomy Manifolds
• Holographic Supergravity Dual to Three Dimensional N=2 Gauge Theory
• Counting RG flows
• Towards Holographic Gravity Dual of N=1Superconformal Chern-Simons Gauge Theory
• Transition of Large $R$-Charge Operators on a Conformal Manifold
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry