arXiv 2008.022932020-08-05hep-th

开弦S-矩阵空间的开拓

Carving out the Space of Open-String S-matrix

Yu-tin Huang, Jin-Yu Liu, Laurentiu Rodina, Yihong Wang

备注：: 13 figures
DOI：: 10.1007/JHEP04(2021)195

摘要：

在本文中，我们探讨了开弦振幅作为时空S-矩阵和一维CFT关联函数的双重作用。我们从两个方向来研究这种对应关系。首先，从一个一般的磁盘被积打扮的Koba-Nielsen因子，我们证明了交换对称性的振幅因子分解残基的被积函数是可扩展的SL（2，R）共形块。此外，与酉性相关的正性约束意味着SL（2，R）块必须以线性组合出现，因此Virasoro块出现在解空间中的“扭结”处。换句话说，Virasoro对称性出现在一致因子分解的边界。接下来，我们考虑低能量EFT描述，其中幺正性表现为耦合必须存在的EFThedron。一个世界表描述的存在意味着，通过Koba-Nielsen因子，单值关系之间的EFT耦合施加代数身份。我们证明在有限的导数阶的“monodromy平面”和EFThedron的交叉点雕刻出一个小岛的耦合，继续缩小的导数阶增加。在八阶导数上，在三维单值平面上，交点将这个岛的宽度固定为关于超级字符串答案的大约1.5 $\%$（$ζ(3)$的）和0.2 $\%$（$ζ(5)$的）。这使我们猜想，四点开超弦振幅可以完全由单值平面和EFThedron相交的几何决定。

英文摘要：

In this paper, we explore the open string amplitude's dual role as a space-time S-matrix and a 1D CFT correlation function. We pursue this correspondence in two directions. First, beginning with a general disk integrand dressed with a Koba-Nielsen factor, we demonstrate that exchange symmetry for the factorization residue of the amplitude forces the integrand to be expandable on SL(2,R) conformal blocks. Furthermore, positivity constraints associated with unitarity imply the SL(2,R) blocks must come in linear combinations for which the Virasoro block emerges at the "kink" in the space of solutions. In other words, Virasoro symmetry arises at the boundary of consistent factorization. Next, we consider the low energy EFT description, where unitarity manifests as the EFThedron in which the couplings must live. The existence of a worldsheet description implies, through the Koba-Nielsen factor, monodromy relations which impose algebraic identities amongst the EFT couplings. We demonstrate at finite derivative order that the intersection of the "monodromy plane" and the EFThedron carves out a tiny island for the couplings, which continues to shrink as the derivative order is increased. At the eighth derivative order, on a three-dimensional monodromy plane, the intersection fixes the width of this island to around 1.5$\%$ (of $ζ(3)$) and 0.2$\%$ (of $ζ(5)$) with respect to the super string answer. This leads us to conjecture that the four-point open superstring amplitude can be completely determined by the geometry of the intersection of the monodromy plane and the EFThedron.

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摘要：

英文摘要：

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