The D^6 R^4 term in type IIB string theory on T^2 and U-duality

Abstract

We propose a manifestly U-duality invariant modular form for the D^6 R^4 interaction in the effective action of type IIB string theory compactified on T^2. It receives perturbative contributions upto genus three, as well as non-perturbative contributions from D-instantons and (p,q) string instantons wrapping T^2. Our construction is based on constraints coming from string perturbation theory, U-duality, the decompactification limit to ten dimensions, and the equality of the perturbative part of the amplitude in type IIA and type IIB string theories. 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. We also obtain parts of the genus one and genus k amplitudes for the D^{2k} R^4 interaction for arbitrary k > 3. We enhance a part of this amplitude to a U-duality invariant modular form.

42 pages, LaTeX

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• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• Poisson equation for the three loop ladder diagram in string theory at genus one
• S-matrix elements from T-duality
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• Supersymmetry constraints on the R^4 multiplet in type IIB on T^2
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