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We generalize the gradient flow equation for field theories with nonlinearlyrealized symmetry. Applying the formalism to super Yang-Mills theory, weconstruct a supersymmetric extension of the gradient flow equation. It can beshown that the super gauge symmetry is preserved in the gradient flow.Furthermore, choosing an appropriate modification term to damp the gaugedegrees of freedom, we obtain a gradient flow equation which is closed withinthe Wess-Zumino gauge.

Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory