D-instantons give non-perturbative contribution to string theory amplitudes which can be computed using world-sheet techniques. However the integrals that appear in this computation often have divergences from corners of the moduli spaces which cannot be tamed by the usual procedure of analytic continuation. We show how using insights from string field theory we can extract finite unambiguous results from these apparently divergent integrals. The Zoom link will be sent by your local Triangle seminar organiser or you can contact bogdan.stefanski.1@city.ac.uk

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. In the critical superstring theory, multi-instanton and multi anti-instanton amplitudes satisfy the reality condition. Contribution to the amplitudes from the instanton anti-instanton sector satisfies the reality condition if we make a specific choice of integration cycle over the configuration space of string fields, whereas contribution due to the non-BPS D-instantons will need to either vanish or have an overall real normalization in order for it to give real contribution. (please email jung-wook.kim AT qmul.ac.uk for the zoom link)