On the chiral anomaly and the Yang-Mills gradient flow

TL;DR

This paper demonstrates that two different universal expressions for topological susceptibility in QCD, one based on the Yang-Mills gradient flow and the other on density-chain correlation functions, are equivalent in the continuum limit across various quark flavors.

Contribution

It establishes the equivalence of gradient flow and density-chain based expressions for topological susceptibility in continuum QCD.

Findings

The two expressions coincide in the continuum limit.

The equivalence holds for any number of quark flavors within the asymptotic freedom range.

Provides a theoretical foundation linking gradient flow and Ward identities.

Abstract

There are currently two singularity-free universal expressions for the topological susceptibility in QCD, one based on the Yang-Mills gradient flow and the other on density-chain correlation functions. While the latter link the susceptibility to the anomalous chiral Ward identities, the gradient flow permits the emergence of the topological sectors in lattice QCD to be understood. Here the two expressions are shown to coincide in the continuum theory, for any number of quark flavours in the range where the theory is asymptotically free.