Worldsheet (anti)instanton bound states in type II on $T^2$

Abstract

The 1/8 BPS $D^6{\mathcal{R}}^4$ coupling in type II string theory compactified on $T^2$ receives contributions from worldsheet instantons and anti-instantons wrapping the $T^2$, 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 $D^6{\mathcal{R}}^4$ 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 $T^2$.

14 pages, LaTeX, v2 supersedes published version

References in corpus (8)

• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• $D^6{R}^4$ amplitudes in various dimensions
• Minimal unitary representations from supersymmetry
• The D^6 R^4 term from three loop maximal supergravity
• Cancellation of divergences up to three loops in exceptional field theory
• SL(2,Z)-invariance and D-instanton contributions to the $D^6{R}^4$ interaction
• 1/8-BPS Couplings and Exceptional Automorphic Functions