D-instanton Effects in Type IIB String Theory

Abstract

We study D-instanton contributions to supergraviton scattering amplitudes in the ten-dimensional type IIB superstring theory beyond the leading non-perturbative order. In particular, we determine the one-D-instanton contribution to maximal R-symmetry violating (MRV) amplitudes with arbitrary momenta at the first subleading order in string coupling, as well as the effects of a D-/anti-D-instanton pair at leading nontrivial order in the momentum expansion. These results confirm a number of predictions of S-duality, and unveil some previously unknown pieces of type IIB string amplitudes.Our computation is based on the Neveu-Schwarz-Ramond formalism with picture changing operators and vertical integration. The naive on-shell prescription for Dinstanton mediated amplitudes, based on integration over the moduli space of worldsheet geometries as well as the moduli space of D-instanton boundary conditions, suffers from potential open string divergences and regularization ambiguities that are in principle resolved in the framework of open+closed superstring field theory. In this paper, the "on-shell ambiguities" of one-D-instanton MRV amplitudes are resolved by arguments involving supersymmetry and soft limits, part of which is verified by a string field theoretic computation in a highly nontrivial manner.

The SAGEX review on scattering amplitudes Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their N=4 supersymmetric Yang–Mills duals

“…is identified with the term of mass dimension 14 in the low-energy expansion of the six-point MUV tree-level amplitude from explicit computation as given in (27). Hence the coefficient F (3) 2,2 (τ , τ ) of the second linear combination O (3) 6,2 does not receive any tree-level contribution but only contains terms originating from higher-genus string amplitudes.…”

The ZZ annulus one-point function in non-critical string theory: A string field theory analysis

“…The string field theory analysis of instanton amplitudes has been extended to other noncritical string models [6][7][8][9][10] where the computations agree precisely with the predictions from the dual matrix models. It has also been extended to critical superstrings [11][12][13][14][15] where the D-instanton effects match precisely with the predictions from superstring JHEP12(2022)151 dualities. In [16], worldsheet computations of instanton effects were performed in Calabi-Yau orientifold compactifications, which is a new result and was not previously known from a dual description.…”

“…Let us denote the amplitude computed using (5.33) with all the external states taken as c by r A, and let r A c denote the contribution to this amplitude from figure5(c) (with just one of the three possible assignments of the external operators to the external legs).First, note that figure5(c) with the internal propagator also being the tachyon, is the product of three factors: the C-O-O amplitude (with the closed string puncture being V and the two open string punctures being tachyons), the tachyon propagator, and the O-O-O three tachyon amplitude. The product of the C-O-O amplitude and the tachyon propagator appears also in figure2(c) and is given by(5.19) 11. The O-O-O tachyon vertex can be computed using the local coordinates in (5.2) and the ghost correlator in (2.1) to be α 3 .…”

Multi-instantons in minimal string theory and in matrix integrals

“…Motivated by the study of instanton effects in the c = 1 string theory [7][8][9][10], as well as critical (superstring) theories [11][12][13][14][15], in our previous work [16] we used tools from string field theory to compute the one-loop normalization constant that multiplies these instanton contributions to various physical quantities. In particular, the genus expansion of the free energy F reads…”