  The chiral phase transition in QCD at finite chemical potential and
temperature can be characterized for small chemical potential by its curvature
and the transition temperature. The curvature is accessible to QCD lattice
simulations, which are always performed at finite pion masses and in finite
simulation volumes. We investigate the effect of a finite volume on the
curvature of the chiral phase transition line. We use functional
renormalization group methods with a two flavor quark-meson model to obtain the
effective action in a finite volume, including both quark and meson fluctuation
effects. Depending on the chosen boundary conditions and the pion mass, we find
pronounced finite-volume effects. For periodic quark boundary conditions in
spatial directions, we observe a decrease in the curvature in intermediate
volume sizes, which we interpret in terms of finite-volume quark effects. Our
results have implications for the phase structure of QCD in a finite volume,
where the location of a possible critical endpoint might be shifted compared to
the infinite-volume case.
