Gradient flow exact renormalization group
Hidenori Sonoda, Hiroshi Suzuki
TL;DR
This paper establishes a precise connection between gradient flow and the exact renormalization group, proposing a gauge-invariant ERG equation for Yang--Mills theory that can be extended to lattice gauge theory.
Contribution
It introduces a gauge-invariant ERG differential equation for Yang--Mills theory inspired by the gradient flow, extending continuum and lattice gauge theory frameworks.
Findings
Connection between gradient flow and ERG in scalar theory
Proposed gauge-invariant ERG equation for Yang--Mills
Extension potential to lattice gauge theory
Abstract
The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of the Wilson action in the exact renormalization group (ERG) formalism. By imitating the structure of this connection, we propose an ERG differential equation that preserves manifest gauge invariance in Yang--Mills theory. Our construction in continuum theory can be extended to lattice gauge theory.
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