Topological Susceptibility and QCD at Finite Theta Angle

TL;DR

This paper introduces the theoretical aspects of topology and theta-dependence in QCD, discusses their phenomenological implications, and reviews analytic predictions and recent lattice simulation results.

Contribution

It provides a comprehensive pedagogical overview of theta-dependence in QCD, combining theoretical approaches with recent numerical findings.

Findings

Analytic predictions for theta-dependence vary across methods.

Lattice simulations offer recent numerical insights into QCD topology.

Phenomenological relevance includes eta' physics and the strong CP problem.

Abstract

In this chapter we provide a pedagogical introduction to the main theoretical aspects related to topology and $\theta$-dependence in Quantum Chromo-Dynamics (QCD), and to their phenomenological relevance in the Standard Model ($\eta^\prime$ physics, neutron electric dipole moment) and beyond (strong CP problem and the axion solution). We then provide an overview of the main analytic predictions for $\theta$-dependence obtained using several different approaches (chiral effective theories, large-$N$ arguments, semiclassical methods) and their regimes of validity, as well as a selection of the most recent numerical results about QCD topology obtained via Monte Carlo simulations of the lattice-discretized theory.