String interactions from matrix string theory

Matrix string theory, i.e. the two-dimensional U(N) SYM with N = (8,8) supersymmetry, has classical BPS solutions that interpolate between an initial and a final string configuration via a bordered Riemann surface. The Matrix string theory amplitudes around such a classical BPS background, in the strong Yang-Mills coupling, are therefore candidates to be interpreted in a stringy way as the transition amplitude between given initial and final string configurations. In this paper we calculate these amplitudes and show that the leading contribution is proportional to the factor gs−χ, where χ is the Euler characteristic of the interpolating Riemann surface and gs is the string coupling. This is the factor one expects from perturbative string interaction theory.