# On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs are always independent.

Also in Gaiotto's class of $N=2$ non-Lagrangian theories, the chiral ring of the Coulomb branch doesn't (seem to) have relations.

Is it a general fact? If so, how can we deduce it from the $N=2$ supersymmetric algebras?

I was asked to clarify the definition of the Coulomb branch in non-Lagrangian theories; let's define them for $N=2$ SCFT by the fact that $SU(2)_R$ symmetry acts on the Coulomb branch operators trivially.

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## protected by ACuriousMindDec 3 '15 at 23:00

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