CONFINING PHASE OF SUPERSTRINGS AND AXIONIC STRINGS

In the four-dimensional effective field theory of the heterotic superstring compactified on a Calabi-Yau manifold, we find a new class of spacetime string instantons in the gravity sector that involves graviton, dilaton, and Kalb-Ramond (axion) fields. The instantons satisfy generalized (anti)self-duality equations, and saturate a Bogomolnyi bound provided by the underlying supersymmetry. The instantons lead to several intriguing nonperturbative phenomena to low-energy string theory. A mass gap is generated to the Kalb-Ramond gauge fields, and results in the confinement of superstrings into Kalb-Ramond domain walls below the compactification scale. More interestingly, they provide a new example of the nonperturbative breakdown of the superpotential nonrenormalization theorem. Together with the world-sheet string instantons, this implies that all would-be Peccei-Quinn symmetries that arise in four-dimensional string theories are completely broken around the string compactification scale. Being self-dual, the instantons provide precisely two gravitino zero modes, thus might induce dynamical supersymmetry breaking. We also point out an underlying analogy with the invisible-axionic domain walls bounded by axionic strings.