  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.
