Penrose Limit and Enhancon Geometry

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We study superstring theories on the Penrose limit of the enhancon geometry realized by the D(p+4)-branes wrapped on a K3 surface. We first examine the null geodesics with fixed radius in general brane backgrounds, which give solvable superstring theories with constant masses. In most cases, the superstring theories contain negative mass-squared. We clarify a condition that the world-sheet free fields have positive mass-squared. We then apply this condition to the enhancon geometry and find that the null geodesics with fixed radius exist only for p=0 case. They define the superstring theories with positive mass-squared. For p>0 case, we show that there is no null geodesic with fixed radius. We also discuss the decoupling limit which gives the dual geometry of super Yang-Mills theory with 8 supercharges. We discuss the K3-volume dependence of the superstring spectrum.