Speaker
Description
In this talk, we explore the QCD vacuum structure with topological theta angle, employing a novel semiclassical framework on $\mathbb{R}^2 \times T^2$ with 't Hooft and baryon magnetic fluxes. Grounded in the adiabatic continuity conjecture, the semiclassical analysis at small $T^2$ can capture the QCD vacuum structure, and the confining vacuum is described by the dilute gas of center vortices. Our 2d effective theory at small $T^2$ explains a plausible $\theta$-dependence of the QCD vacuum: (1) The one-flavor QCD exhibits the $CP$-broken two-fold degenerate vacua at $\theta =\pi$ for quark mass above a critical value, and (2) the multi-flavor QCD shows the $CP$-breaking at $\theta =\pi$ for all (degenerate) quark masses. This 2d effective theory can be regarded as a 2d analog of the chiral Lagrangian with periodicity-extended eta prime. Intuitively, eta prime extends its periodicity by "eating" the $\mathbb{Z}_N$ SPT label of the $SU(N)$ Yang-Mills vacuum. Based on this observation, we point out that the periodicity extension of eta prime can improve the consistency of the $4$d chiral Lagrangian with known global structures, such as discrete anomalies.
