Topological insulators and the QCD vacuum: the theta parameter as a Berry phase

Understand

There is considerable evidence, based on large $N_c$ chiral dynamics, holographic QCD, and Monte Carlo studies, that the QCD vacuum is permeated by discrete quasivacua separated by domain walls across which the local value of the topological $\theta$ parameter jumps by $\pm2\pi$.

• In the 2-dimensional $CP^{N-1}$ sigma model, a pointlike charge is a domain wall, and $\theta$ describes the background electric flux and the polarization of charged pairs in the vacuum.
• We show that the screening process, and the role of $\theta$ as an order parameter describing electric polarization, are naturally formulated in terms of Bloch wave eigenstates of the Dirac Hamiltonian in the background gauge field.
• This formulation is similar to the Berry phase description of electric polarization and quantized charge transport in topological insulators.