The D^4 R^4 term in type IIB string theory on T^2 and U-duality

Understand

We propose a manifestly U-duality invariant modular form for the D^4 R^4 interaction in type IIB string theory compactified on T^2.

• It receives perturbative contributions upto two loops, and non-perturbative contributions from D-instantons and (p,q) string instantons wrapping T^2.
• We provide evidence for this modular form by showing that the coefficients at tree level and at one loop precisely match those obtained using string perturbation theory.
• Using duality, parts of the perturbative amplitude are also shown to match exactly the results obtained from eleven dimensional supergravity compactified on T^3 at one loop.