Generalized Gradient Flow Equation and Its Applications

TL;DR

This paper introduces a generalized gradient flow equation applicable to quantum field theories with nonlinear symmetries, demonstrating its utility in supersymmetric gauge theories and nonlinear sigma models, with non-perturbative finiteness results.

Contribution

It develops a new generalized gradient flow framework for theories with nonlinear symmetries and applies it to supersymmetric Yang-Mills and sigma models, showing non-perturbative finiteness.

Findings

Constructed a supersymmetric gradient flow in Wess-Zumino gauge.

Demonstrated non-perturbative finiteness of the two-point function in the sigma model.

Applied the generalized flow to different models, showing broad applicability.

Abstract

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.