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

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

2007-08-22

arxiv.org/abs/0708.2950v2

Phys.Rev.D77:106003,2008

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, LaTeX

Scientific paper

10.1103/PhysRevD.77.106003

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. Decompactifying the theory to nine dimensions, we obtain a U-duality invariant modular form, whose coefficients at tree level and at one loop agree with string perturbation theory.

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