A vacuum of a globally supersymmetric gauge theory preserves supersymmetry exactly when every auxiliary F-field and D-field can vanish simultaneously. Its vacuum energy is then zero because the scalar potential is a sum of nonnegative squares.
D-flatness sets every vector-multiplet auxiliary field to zero. Quotienting its solution set by the compact gauge group is equivalent, under standard stability conditions, to quotienting the F-flat variety by the complexified gauge group.
The vacuum moduli space is the space of simultaneous F-flat and D-flat configurations modulo gauge transformations. Gauge-invariant chiral operators often provide holomorphic coordinates, subject to algebraic constraints.
A Higgs branch is a component on which charged scalar expectation values break some or all of the gauge group. It is often obtained as a Kähler or hyperkähler quotient.
A Coulomb branch is a component on which scalar expectation values in vector or neutral multiplets leave an Abelian gauge sector unbroken. Charged fields can become massless at special points where additional branches meet it.
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