U-duality and D-brane Combinatorics

TL;DR

This paper explores non-perturbative D-brane instanton effects on R^4 couplings in toroidal compactifications, deriving configurations and weights through T-duality and analyzing their relation to U-duality and geometric interpretations.

Contribution

It provides a detailed derivation of D-brane instanton contributions to R^4 couplings and establishes rules for their weighting, extending understanding of non-perturbative effects in string compactifications.

Findings

Derived non-perturbative corrections from supergravity amplitudes.

Identified D-brane configurations as bound states and fluxes.

Linked D-brane instantons to U-duality relations.

Abstract

We investigate D-brane instanton contributions to R^4 couplings in any toroidal compactification of type II theories. Starting from the 11D supergravity one-loop four-graviton amplitude computed by Green, Gutperle and Vanhove, we derive the non-perturbative O(e^{-1/\lambda}) corrections to R^4 couplings by a sequence of T-dualities, and interpret them as precise configurations of bound states of D-branes wrapping cycles of the compactification torus. Dp-branes explicitely appear as fluxes on D(p+2)-branes, and as gauge instantons on D(p+4)-branes. Specific rules for weighting these contributions are obtained, which should carry over to more general situations. Furthermore, it is shown that U-duality in D<=6 relates these D-brane configurations to O(e^{-1/\lambda^2}) instantons for which a geometric interpretation is still lacking.