Non-BPS interactions from the type II one loop four graviton amplitude

TL;DR

This paper derives T-duality invariant differential equations for specific non-BPS interactions in type II string theory from one-loop four graviton amplitudes, revealing their structure and solutions in nine dimensions.

Contribution

It provides the first derivation of T-duality invariant equations for non-BPS interactions from string amplitudes, including explicit solutions in nine dimensions.

Findings

Derived T-duality invariant differential equations for D8R4 and D10R4 interactions.

Identified source terms involving bulk and boundary contributions in the equations.

Explicitly solved the equations in nine-dimensional compactification.

Abstract

We obtain T--duality invariant second order differential equations satisfied by the $D^8\mathcal{R}^4$ and $D^{10} \mathcal{R}^4$ interactions from the low energy expansion of the one loop four graviton amplitude in toroidally compactified type II string theory. The eigenvalues of these equations are completely determined by the structure of the one loop integrands. Unlike the BPS interactions, these non--BPS interactions satisfy Poisson equations having source terms that receive contributions from both the bulk and boundary of the worldsheet moduli space. We explicitly solve these equations in nine dimensions.