Worldsheet (anti)instanton bound states in type II on T2

Abstract

The 1/8 BPS D⁶ℛ⁴ coupling in type II string theory compactified on T² receives contributions from worldsheet instantons and anti-instantons wrapping the T², up to genus three in string perturbation theory. These involve contributions separately from bound states of instantons and anti-instantons, which are qualitatively similar to such contributions to the 1/2 and 1/4 BPS couplings. At genus two, the D⁶ℛ⁴ coupling also receives contributions from instanton/anti-instanton bound states unlike the 1/2 and 1/4 BPS couplings, which is a consequence of a T-duality invariant eigenvalue equation a term in the coupling satisfies. We solve this eigenvalue equation to obtain the complete structure of the worldsheet (anti)instanton contributions. In the type IIB theory, strong weak coupling duality leads to certain contributions involving bound states of D string (anti)instantons wrapping the T².