Influence of vector interactions on the favored shape of inhomogeneous chiral condensates

We update a previous study of the effects of vector interactions in the Nambu–Jona-Lasinio model on the formation of inhomogeneous chiral symmetry breaking condensates. In particular, by properly considering a spatially modulated vector mean field associated with the quark number density of the system we show that, as the value of the vector coupling increases, a chiral density wave modulation can become thermodynamically favored over a real sinusoidal modulation. This behavior is found both via a GinzburgLandau analysis close to the Lifshitz point, as well as with a full numerical diagonalization of the meanfield Dirac Hamiltonian at vanishing temperature.