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On Renormalization Group Flows and Exactly Marginal Operators in Three Dimensions
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In this article, 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 a marginal operator may be guessed using mirror symmetry.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.read more
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Nathan Seiberg,Nathan Seiberg +1 more
TL;DR: In this article, the authors demonstrate electric-magnetic duality in N = 1 supersymmetric non-Abelian gauge theories in four dimensions by presenting two different gauge theories leading to the same non-trivial long distance physics.
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