1/2 BPS 三点函数的开-闭-开三重性
Open-Closed-Open Triality for 1/2 BPS Three-Point Functions
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中文总结 AI 辅助
本文建立四维N=4超杨-米尔斯理论半BPS三点函数的开-闭-开三重性，构建V型与F型开弦模型，通过精确有限N多项式等检验对应关系，关联三色Strebel曲面与Belyi映射等靶空间构造。
中文摘要 AI 辅助
开-闭-开三重性通过共同的闭弦理论关联两种不同的开弦描述。本文针对四维$\boldsymbol{\text{N}=4}$超杨-米尔斯理论中受保护的半BPS三点函数，建立了开-闭-开三重性。从代表巨引力子的行列式插入出发，我们构建了一种V型开弦高斯三矩阵模型，并通过色味变换，推导得到由形成三角箭图的三个双基本矩阵构成的F型开弦模型。其闭箭图行走包含定向三次循环，这是二分两点情形所不具备的特征。我们通过推导精确的有限$N$单巨多项式、复现已知的F型大$N$鞍点，以及通过其组合数据的显式双射证明V型与F型特征展开的等价性，检验了该对应关系。在闭弦侧，连通三矩阵收缩决定了三色整数Strebel曲面。我们认为，对应的靶空间构造可由重心细分的Belyi映射或着色Hurwitz星自然描述。
英文摘要
Open-closed-open triality relates two distinct open string descriptions through a common closed string theory. In this paper, we develop an open-closed-open triality for protected half-BPS three-point functions in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory. Starting from determinant insertions representing giant gravitons, we formulate a V-type open-string Gaussian three-matrix model and, through a color-flavor transformation, derive an F-type open-string model of three bifundamental matrices forming a triangular quiver. Its closed quiver walks include oriented cubic cycles, a feature absent from the bipartite two-point case. We test the correspondence by deriving exact finite-$N$ single-giant polynomials, recovering the known F-type large-$N$ saddles, and proving the equivalence of the V- and F-type character expansions via an explicit bijection of their combinatorial data. At the closed string corner, connected three-matrix contractions determine three-colored integer Strebel surfaces. We argue that the corresponding target-space construction is naturally described by a barycentrically subdivided Belyi map or a colored Hurwitz constellation.
发表机构
- The University of Osaka（大阪大学）
- University of Tokyo（东京大学）
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