Multi-instanton calculus in c = 1 string theory

Abstract

We formulate a strategy for computing the complete set of non-perturbative corrections to closed string scattering in c = 1 string theory from the worldsheet perspective. This requires taking into account the effect of multiple ZZ-instantons, including higher instantons constructed from ZZ boundary conditions of type (m, 1), with a careful treatment of the measure and contour in the integration over the instanton moduli space. The only a priori ambiguity in our prescription is a normalization constant mathcal{N} m that appears in the integration measure for the (m, 1)-type ZZ instanton, at each positive integer m. We investigate leading corrections to the closed string reflection amplitude at the n-instanton level, i.e. of order {e}^{-n/{g}_s} , and find striking agreement with our recent proposal on the non-perturbative completion of the dual matrix quantum mechanics, which in turn fixes mathcal{N} m for all m.