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arXiv 0712.1252hep-th
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T^2上IIB弦论中的D^6 R^4项和U-对偶

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

Anirban Basu

摘要:

在T^2上紧化的IIB型弦论的有效作用量中,我们提出了D^6 R^4相互作用的一个明显的U-对偶不变模形式。它接受到亏格3的微扰贡献,以及包裹T^2的D-瞬子和(p,q)弦瞬子的非微扰贡献。我们的构造是基于弦微扰理论、U-对偶性、10维的解压缩极限以及IIA型和IIB型弦论中振幅微扰部分的相等性的约束。利用对偶性,部分微扰振幅也被证明与在T^3上在一个圈上紧化的11维超引力所得到的结果完全匹配。我们还得到了任意k > 3时D^{2k} R^4相互作用的亏格1和亏格k振幅的一部分。我们提高了这个幅度的一部分,一个U-对偶不变的模形式。

英文摘要:

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.

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