  We propose a generalization of the gradient flow equation for quantum field
theories with nonlinearly realized symmetry. Applying the equation to
$\mathcal{N}=1$ $SU(N)$ super Yang-Mills theory in four dimensions, we
construct a supersymmetric extension of the gradient flow equation. Choosing an
appropriate modification term to damp the gauge degree of freedom, we obtain a
gradient flow equation which is closed within the Wess-Zumino gauge. We also
apply the equation to the $O(N)$ nonlinear sigma model in two dimensions at
large $N$, and show that the two point function in terms of the flowed field is
non-perturbatively finite.

High Energy Physics - Lattice;High Energy Physics - Theory