Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Yang--Mills $β$ function in the gradient flow exact renormalization group

Sorato Nagao, Hiroshi Suzuki

Abstract

The gradient flow exact renormalization (GFERG) is a variant of the exact renormalization group of gauge theory that aims to preserve gauge symmetry as manifestly as possible. From an integral representation of the Wilson action in GFERG for the Yang--Mills theory, we explicitly compute the one-loop renormalization group functions that reproduce correct coefficients. From the correspondence with the gradient flow formalism by Lüscher and Weisz, we also argue that GFERG reproduces the conventional renormalization group functions in all orders of perturbation theory.

Yang--Mills $β$ function in the gradient flow exact renormalization group

Abstract

The gradient flow exact renormalization (GFERG) is a variant of the exact renormalization group of gauge theory that aims to preserve gauge symmetry as manifestly as possible. From an integral representation of the Wilson action in GFERG for the Yang--Mills theory, we explicitly compute the one-loop renormalization group functions that reproduce correct coefficients. From the correspondence with the gradient flow formalism by Lüscher and Weisz, we also argue that GFERG reproduces the conventional renormalization group functions in all orders of perturbation theory.

Paper Structure

This paper contains 11 sections, 73 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Yang--Mills $\beta$ function in GFERG
  3. Wilson action in GFERG
  4. Renormalization group functions
  5. Higher orders
  6. Conclusion
  7. Feynman rule for correlation functions under the functional integral \ref{['eq:(2.2)']}
  8. Perturbative solution to flow equations
  9. Quantum propagators
  10. Vertices
  11. Calculation of diagrams in Fig. \ref{['fig:1']}

Figures (2)

  • Figure 1: One-loop level diagrams which contribute to the two-point function \ref{['eq:(2.28)']}.
  • Figure 2: One-loop level diagrams which contribute to the two-point function \ref{['eq:(2.28)']}. Shaded blob vertices are the effect of the mass term arising from the Gaussian factors.