  To incorporate the effect of gluons on the evolution dynamics of the quark
matter produced in relativistic heavy-ion collisions, we extend the 3-flavor
Nambu-Jona-Lasinio (NJL) transport model to include the contribution from the
Polyakov loops. Imbedding the resulting pNJL partonic transport model in an
extended multiphase transport (extended AMPT) model, we then study the elliptic
flow splittings between particles and their antiparticles in relativistic
heavy-ion collisions at RHIC-BES energies. We find that a weak quark vector
interaction in the partonic phase is able to describe the elliptic flow
splitting between protons and antiprotons in heavy-ion collisions at
$\sqrt{s_{NN}}=7.7$ to 39 GeV. Knowledge on the quark vector interaction is
useful for understanding the equation of state of quark matter at large baryon
chemical potentials and thus the location of the critical point in the QCD
phase diagram.
