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

Abstract

We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that the super gauge symmetry is preserved in the gradient flow. Furthermore, choosing an appropriate modification term to damp the gauge degrees of freedom, we obtain a gradient flow equation which is closed within the Wess-Zumino gauge.

35 pages, v2: typos corrected and references added, v3: published version

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Cited by in corpus (19)

• Gradient flow and the renormalization group
• Gradient Flow of O(N) nonlinear sigma model at large N
• A study of center and chiral symmetry realization in thermal $\mathcal{N}=1$ super Yang-Mills theory using the gradient flow
• Background field method in the gradient flow
• Gradient flow exact renormalization group
• Geometries from field theories
• 4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow
• Supersymmetric gradient flow in the Wess-Zumino model
• Topological Susceptibility of the 2d O(3) Model under Gradient Flow
• Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang--Mills supercurrent
• Flow Equation of N=1 Supersymmetric O(N) Nonlinear Sigma Model in Two Dimensions
• Supersymmetric gradient flow in 4d N=1 SQCD
• Axial $U(1)$ anomaly in a gravitational field via the gradient flow
• A basis of the gradient flow exact renormalization group for gauge theory
• Two-loop gradient-flow renormalization of scalar QCD
• Perturbative analysis of the Wess-Zumino flow
• Topology of the O(3) non-linear sigma model under the gradient flow
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking
• 4D $\mathcal{N}=1$ SYM supercurrent on the lattice in terms of the gradient flow