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arXiv 2409.09561hep-th
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论超几何振幅的幺正性

On Unitarity of the Hypergeometric Amplitude

Gareth Mansfield, Marcus Spradlin

备注：
Based on a Brown University undergraduate thesis, 37 pages, 6 figures; v2: minor corrections and improvements
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AI总结：

本文将超几何振幅推广到I型超弦理论，通过排除非幺正参数区域并证明另一大片参数空间中分波系数为正，系统研究了其幺正性，并推广了Veneziano振幅分波系数的正性结果。

摘要：

超几何振幅是玻色弦理论中四点快子散射的Veneziano振幅的单参数形变，且与S矩阵自举约束相容。本文为I型超弦理论构造了类似的Veneziano振幅超几何推广。随后我们排除了(r,m^2,D)参数空间中的一大片非幺正区域，并确立了另一大片(r,m^2,D)参数空间子集，其中所有留数的分波系数均为正。我们还分析了各种极限和特殊情况下的正性。作为我们分析的一个推论，我们能够直接证明比别处已给出的更广泛的一组Veneziano振幅分波系数的正性。

英文摘要：

The hypergeometric amplitude is a one-parameter deformation of the Veneziano amplitude for four-point tachyon scattering in bosonic string theory that is consistent with $S$-matrix bootstrap constraints. In this article we construct a similar hypergeometric generalization of the Veneziano amplitude for type-I superstring theory. We then rule out a large region of the $(r,m^2,D)$ parameter space as non-unitary, and establish another large subset of the $(r, m^2, D)$ parameter space where all of the residue's partial wave coefficients are positive. We also analyze positivity in various limits and special cases. As a corollary to our analysis, we are able to directly demonstrate positivity of a wider set of Veneziano amplitude partial wave coefficients than what has been presented elsewhere.

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