Duality and higher derivative terms in M theory
Duality and higher derivative terms in M theory
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M 理论中的对偶性和高阶导数项
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
P. Vanhove
中科院分区：
文献类型：
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作者：
M. Green;P. Vanhove
利用M-理论的对偶性确定了IIA和IIB超弦有效作用量对D 6 4相互作用耦合常数的精确依赖性。当提升到11维时，这决定了11维M理论中D 6 4相互作用的系数。这些结果是通过考虑在圆和环面上紧化的11维超引力中的四引力子双圈散射振幅得到的，推广了以前关于低导数相互作用的结果。环面的紧化导致一个有趣的SL（2，）-不变函数的环面的复杂结构（IIB弦耦合），满足一个拉普拉斯方程的源项上的模空间的基本域。这个方程的结构雅阁一般的超对称性考虑，并直接决定了在微扰IIB弦理论中对D 64的树级和单圈贡献，这与弦理论的显式计算一致，以及在弦理论中尚未得到的双圈和三圈贡献。拉普拉斯方程的完全解除了微扰项外，还包含单D瞬子和双D瞬子贡献的无穷级数。对11维超引力的高阶环图的一般考虑表明，这些结果可以扩展到低能展开中的高阶相互作用。
Dualities of M-theory are used to determine the exact dependence on the coupling constant of the D6 4 interaction of the IIA and IIB superstring effective action. Upon lifting to eleven dimensions this determines the coefficient of the D6 4 interaction in eleven-dimensional M-theory. These results are obtained by considering the four-graviton two-loop scattering amplitude in eleven-dimensional supergravity compactified on a circle and on a two-torus — extending earlier results concerning lower-derivative interactions. The torus compactification leads to an interesting SL(2,)-invariant function of the complex structure of the torus (the IIB string coupling) that satisfies a Laplace equation with a source term on the fundamental domain of moduli space. The structure of this equation is in accord with general supersymmetry considerations and immediately determines tree-level and one-loop contributions to D64 in perturbative IIB string theory that agree with explicit string calculations, and two-loop and three-loop contributions that have yet to be obtained in string theory. The complete solution of the Laplace equation contains infinite series' of single D-instanton and double D-instanton contributions, in addition to the perturbative terms. General considerations of the higher loop diagrams of eleven-dimensional supergravity suggest extensions of these results to interactions of higher order in the low energy expansion.