Elucidating the Vacuum Structure of the Aoki Phase

Abstract

In this paper, we discuss the vacuum structure of QCD with two flavors of Wilson fermions, inside the Aoki phase. We provide numerical evidence, coming from HMC simulations in $4^4$, $6^4$ and $8^4$ lattices, supporting a vacuum structure for this model at strong coupling more complex than the one assumed in the standard wisdom, with new vacua where the expectation value of $i\bar{\psi }{\gamma }_5\psi$ can take non-zero values, and which can not be connected with the Aoki vacua by parity-flavour symmetry transformations.

Comments: 27 pages, 8 figures, 4 tables, v2: 1. Modifies abstract and layout and 2. revises conclusions, v3: Includes new section with discussion on our results and WChPT, other minor modifications, v4: Introduces new section discussing the presence of critical lines within the Aoki phase