Meson strings and flavor branes

We investigate the shape of meson strings in the five-dimensional curved space and the potential between the quark and anti-quark in a QCD-like string model based on D6 flavor branes in the presence of D4 color branes wrapping one of the compactified dimension on an S-1. The flavor branes on which both ends of a meson string lie are assumed to be separated in this five dimensional space, depending. on the values of the constituent quark masses. It is shown in this picture that a meson string with different flavors at two ends changes shape at a critical distance. There is, however, no critical distance for a meson with the same flavor. At this critical distance, the potential between a quark and an anti-quark with different flavors gives a point of reflection and changes shape near this point. Accordingly, the attractive force between a quark and an anti-quark seems to become stronger when the distance between the flavor branes connecting meson strings becomes larger. This indicates that quark systems with different flavors can form high-density states.