String Interactions in a Plane-Fronted Parallel-Wave Spacetime

We argue that string interactions in a plane-fronted parallel-wave spacetime are governed by an effective coupling $g_{\mathrm{e}\mathrm{f}\mathrm{f}}=g_s(\mu p^{+}{\alpha }^{\prime })f(\mu p^{+}{\alpha }^{\prime })$ where $f(\mu p^{+}{\alpha }^{\prime })$ is proportional to the light-cone energy of the string states involved in the interaction. This simply follows from generalities of a matrix string description of this background. $g_{\mathrm{e}\mathrm{f}\mathrm{f}}$ nicely interpolates between the expected result ($g_s$) for flat space (small $\mu p^{+}{\alpha }^{\prime }$) and a recently conjectured expression from the perturbative gauge theory side (large $\mu p^{+}{\alpha }^{\prime }$).