Long Strings and Chiral Non-Singlets in Matrix Quantum Mechanics

We study the non-singlet sectors of Matrix Quantum Mechanics in application to two-dimensional string theory. We use the chiral formalism, which operates directly with incoming and outgoing asymptotic states, related by a scattering operator. We argue that a general non-singlet scattering amplitude decomposes into scattering amplitudes in the adjoint. In the adjoint representation, we express the phase of the tree-level scattering amplitude as an integral over the Fermi sea. We claim that this expression holds for any, in general time-dependent, profile of the Fermi sea. In the case of stationary Fermi sea our formula reproduces Maldacena's scattering amplitude for a long string to go in and come back to infinity.