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We show how repulsive interactions of deconfined quarks as well as confinedhadrons have an influence on the baryon number susceptibilities and thecurvature of the chiral pseudo critical line in effective models of QCD. Wediscuss implications and constraints for the vector interaction strength fromcomparisons to lattice QCD and comment on earlier constraints, extracted fromthe curvature of the transition line of QCD and compact star observables. Ourresults clearly point to a strong vector repulsion in the hadronic phase andnear-zero repulsion in the deconfined phase.

Do lattice data constrain the vector interaction strength of QCD?