Strings from Feynman Graph counting : without large N
Strings from Feynman Graph counting : without large N
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Feynman Graph 计数中的字符串：没有大 N
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
S. Ramgoolam
中科院分区：
文献类型：
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作者：
R. Koch;S. Ramgoolam
一个著名的连接n弦缠绕在一个圆圈和排列的n个对象发挥了根本作用的弦理论的大N二维杨米尔斯理论和其他地方的拓扑和物理弦理论。费曼图计数中的基本问题可以用置换群来优雅地表达。我们表明，这些置换技术费曼图计数，沿着与伯恩赛德计数引理，导致费曼图的计数问题之间的平等性标量场理论和量子电动力学与弦理论与环面或圆柱体目标空间的振幅计数。这种弦理论产生于二维杨米尔斯的大N展开，与具有Sn规范群的格点规范理论密切相关。我们收集和推广了费曼图计数的生成函数的结果，这些结果直接与字符串图像相联系。我们建议，弦组合学和排列之间的连接的影响QFT弦对偶，超出了大N规范理论的框架。
A well-known connection between n strings winding around a circle and permutations of n objects plays a fundamental role in the string theory of large N two dimensional Yang Mills theory and elsewhere in topological and physical string theories. Basic questions in the enumeration of Feynman graphs can be expressed elegantly in terms of permutation groups. We show that these permutation techniques for Feynman graph enumeration, along with the Burnside counting lemma, lead to equalities between counting problems of Feynman graphs in scalar field theories and Quantum Electrodynamics with the counting of amplitudes in a string theory with torus or cylinder target space. This string theory arises in the large N expansion of two dimensional Yang Mills and is closely related to lattice gauge theory with S_n gauge group. We collect and extend results on generating functions for Feynman graph counting, which connect directly with the string picture. We propose that the connection between string combinatorics and permutations has implications for QFT-string dualities, beyond the framework of large N gauge theory.