Generalized Gradient Flow Equation and Its Applications

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.

7 pages, Proceedings of The 33rd International Symposium on Lattice Field Theory 14-18 July 2015 Kobe International Conference Center, Kobe, Japan

References in corpus (5)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Chiral symmetry and the Yang--Mills gradient flow
• Gradient Flow of O(N) nonlinear sigma model at large N
• Encoding field theories into gravities