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

TL;DR

This paper explores non-perturbative effects in type IIB superstring theory, showing how D-instantons and $(p,q)$-strings contribute, and establishes non-renormalization theorems and constraints on higher derivative interactions using dualities.

Contribution

It introduces a non-renormalization theorem for eight-derivative interactions and constrains the form of higher derivative terms in M-theory based on $SL(2,Z)$ symmetry.

Findings

D-instanton effects can be understood as $(p,q)$-string effects.

Only certain $R^{6N+4}$ terms appear in M-theory, with specific loop order contributions.

Non-renormalization theorem restricts interactions to tree-level and one-loop for certain fields.

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.