D-Instanton Corrections as (p,q)-String Effects and Non-Renormalization Theorems

TL;DR

The paper addresses how higher-derivative corrections in Type IIB string theory can be understood through S-duality and dual objects, notably interpreting non-perturbative effects as sums over $(p,q)$-strings. By constructing $SL(2,\mathbb{Z})$-invariant orbits and introducing modular functions $f_k(\tau,\bar{\tau})$, it shows that eight-derivative bosonic terms receive only tree-level and one-loop perturbative corrections, with RR and non-perturbative pieces organized by the same duality structure. It further constrains eleven-dimensional uplift via M-theory, showing that perturbative RR contributions do not spoil the non-renormalization pattern and that $R^{3m+1}$ interactions exist only for odd $m$, implying $R^{6N+4}$ terms at loops $N$ and $2N+1$ in M-theory reductions. A fermionic example ($\lambda^{16}$) is analyzed and found consistent with M-theory expectations, reinforcing a duality-driven unification of perturbative and non-perturbative physics in the IIB effective action.

Abstract

We discuss higher derivative interactions in the type IIB superstring in ten dimensions. From the fundamental string point of view, the non-perturbative corrections are due to D-instantons. We argue that they can alternatively be understood as arising from $(p,q)$-strings. We derive a non-renormalization theorem for eight-derivative bosonic interactions, which states that terms involving either NS-NS or R-R fields occur at tree-level and one-loop only. By using the $SL(2, Z)$ symmetry of M-theory on $T^2$, we show that in order for the possible $R^{3m+1} (m=1,2,...)$ interactions in M-theory to have a consistent perturbative expansion in nine dimensions, $m$ must be odd. Thus, only $R^{6N+4} (N=0,1,...)$ terms can be present in M-theory and their string theory counterparts arise at $N$ and $2N+1$ loops. Finally, we treat an example of fermionic term.