The clash of positivities in topological density correlators

TL;DR

This paper examines the apparent conflict between reflection positivity and topological susceptibility positivity in certain quantum field theories, analyzing lattice correlators and their behavior under different theoretical scenarios.

Contribution

It reveals how the conflict can be resolved within both asymptotic freedom and critical point scenarios, constraining the short-distance behavior of lattice correlators.

Findings

Restrictions on lattice correlator behavior are compatible with asymptotic freedom.

Restrictions are also compatible with a finite-coupling critical point scenario.

The conflict is present even at the lattice level, influencing theoretical models.

Abstract

We discuss the apparent conflict between reflection positivity and positivity of the topological susceptibility in two-dimensional nonlinear sigma models and in four-dimensional gauge theories. We pay special attention to the fact that this apparent conflict is already present on the lattice; its resolution puts some nontrivial restrictions on the short-distance behavior of the lattice correlator. It is found that these restrictions can be satisfied both in the case of asymptotic freedom and the dissident scenario of a critical point at finite coupling.