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.
Highlights
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
As long as t > 0, the sectors are independent of the flow time and so is the topological susceptibility χflt = Q2t /V
The expression provides a regularization-independent definition of the susceptibility, which is close to its naive definition, but properly deals with the fluctuations of the gauge field and the associated ultraviolet singularities
Summary
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. 2. The gradient-flow and the density-chain expression for the topological susceptibility, χflt and χdt c, are both well defined and unambiguously normalized, but they refer to different aspects of the theory, the first characterizing the distribution of the topological charge Qt in the functional integral, while the second derives from an essentially algebraic property of the theory (the anomalous chiral symmetry).
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