The clash of positivities in topological density correlators

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.

arXiv comment10 pages

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Cited by in corpus (5)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Matter of resolution: from quasiclassics to fine tuning
• On the Continuum Limit of Topological Charge Density Distribution
• Shrinking fermionic modes, on the lattice and in the continuum
• Perturbation theory for O(3) topological charge correlators