Some Remarks on the Finitude of Quiver Theories
Some Remarks on the Finitude of Quiver Theories
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发表时间：
1999-11
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通讯作者：
Yang-Hui He
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作者：
Yang-Hui He
D-膜探测、Hanany-Witten装置和几何工程是当前流行的从弦理论构造规范理论的技术的一个分支。同时，渐近自由、有限性和IR自由构成了量子场论中β函数行为的一个可分割性。与之平行的是集合论中有限、驯服和狂野的表示类型的一个可分性。在上述理论的交叉点上是颤抖理论。我们简要地回顾了物理学和数学的一些术语标准。然后我们利用图论和路代数的公理表示理论的某些结果来解决一些物理问题，如图可加性对规范理论的有限性的影响，构造完全IR自由弦轨道理论的不可能性和N<2的四维Yang-Mills理论的不可分类性。
D-brane probes, Hanany-Witten setups and geometrical engineering stand as a trichotomy of the currently fashionable techniques of constructing gauge theories from string theory. Meanwhile, asymptotic freedom, finitude and IR freedom pose as a trichotomy of the beta-function behaviour in quantum field theories. Parallel thereto is a trichotomy in set theory of finite, tame and wild representation types. At the intersection of the above lies the theory of quivers. We briefly review some of the terminology standard to the physics and to the mathematics. Then we utilise certain results from graph theory and axiomatic representation theory of path algebras to address physical issues such as the implication of graph additivity to finiteness of gauge theories, the impossibility of constructing completely IR free string orbifold theories and the unclassifiability of N<2 Yang-Mills theories in four dimensions.