Cutkosky Rules and Unitarity (Violation) in D-instanton Amplitudes

Understand

In perturbative amplitudes in quantum field theory and string field theory, Cutkosky rule expresses the anti-hermitian part of a Feynman diagram in terms of sum over all its cut diagrams, and this in turn is used to prove unitarity of the theory.

• For D-instanton contribution to a string theory amplitude, the cutting rule needed for the proof of unitarity is somewhat different; we need to sum over only those cut diagrams for which all the world-sheet boundaries ending on some particular D-instanton lie on the same side of the cut.
• By working with the closed string effective action, obtained after integrating out the open string modes, we prove that the D-instanton amplitudes actually satisfy these cutting rules, provided the effective action is real.
• The violation of unitarity in the closed string sector of two dimensional string theory can be traced to the failure of this reality condition.