On Mirror Symmetry in Three Dimensional Abelian Gauge Theories

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Abstract

We present an identity relating the partition function of N=4 supersymmetric QED to that of its dual under mirror symmetry. The identity is a generalized Fourier transform. Many known properties of abelian theories can be derived from this formula, including the mirror transforms for more general gauge and matter content. We show that N=3 Chern-Simons QED and N=4 QED with BF-type couplings are conformal field theories with exactly marginal couplings. Mirror symmetry acts on these theories as strong-weak coupling duality. After identifying the mirror of the gauge coupling (sometimes called the ``magnetic coupling'') we construct a theory which is exactly mirror -- at all scales -- to N=4 SQED. We also study vortex-creation operators in the large \(N_f\) limit.

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Is Open Access

Mirror Symmetry in Three Dimensional Gauge Theories

N. Seiberg, K. Intriligator (1996)

We discuss non-trivial fixed points of the renormalization group with dual descriptions in \(N=4\) gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding \(ADE\) gauge group. In particular, we show that in three dimensions small \(E_8\) instantons in string theory are described by a local quantum field theory.