Abstract
Axial anomaly and nesting is elucidated in the context of the inhomogeneous chiral phase. Using the Gross-Neveu models in 1+1 dimensions, we shall discuss axial anomaly and nesting from two different points of view: one is homogeneous chiral transition and the other is the Ferrel-Fulde-Larkin-Ovchinnikov (FFLO) state in superconductivity, which are closely related to each other by way of duality. It is shown that axial anomaly leads to a particular kind of the FFLO state within the two dimensional Nambu-Jona Lasinio model, where axial anomaly is manifested in a different mode. Nesting is a driving mechanism for both phenomena, but its realization has different features. We reconsider the effect of nesting in the context of duality.
Highlights
Nowadays understanding of the QCD phase diagram is one of the main subjects in nuclear physics
Recent lattice QCD simulations have suggested that qqscalar condensate is reduced and chiral symmetry is suggested to be restored at high temperature, and many model calculations have shown that it is restored at high density, by using effective models such as the Nambu-Jona Lasinio (NJL) model or Schwinger-Dyson approach [2]
We have seen that the NJL2 model has Uð1ÞL × Uð1ÞR symmetry in the classical level, but symmetry is broken due to axial anomaly in the presence of the gauge field, Uð1ÞL× Uð1ÞR → UVð1Þ
Summary
Nowadays understanding of the QCD phase diagram is one of the main subjects in nuclear physics. Such transition may give an important impact on the theoretical studies of the QCD phase diagram or some observations in high-energy heavy-ion collisions or compact stars; the Lifshitz point in the QCD phase diagram, spontaneous magnetization of iCP [7], or solidification of quark matter is an example. It is well-known that nesting plays an important role for the appearance of iCP.
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