高维全顶点代数与共形协变关联函数系统
Higher-dimensional full vertex algebras and systems of conformally covariant correlation functions
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中文总结 AI 辅助
本文为紧致d维共形场论构造欧几里得关联函数系统，引入共形d-顶点代数并证明其存在性，且对d≥2给出广义自由标量场的例子，涵盖幺正与非幺正情形。
中文摘要 AI 辅助
我们为紧致$d$维共形场论（不一定是幺正的）构造了一类欧几里得关联函数系统。我们还引入了共形$d$-顶点代数，即全顶点代数的$d$维类比，并证明了从每个共形协变关联函数系统都可以得到这样的代数。最后，对于每个$d\geq 2$，我们构造了一族满足这些公理的例子，对应于广义自由标量场。对于$d>2$，这一族同时包含幺正和非幺正的例子。
英文摘要
We formulate a class of systems of Euclidean correlation functions for compact $d$-dimensional conformal field theories which are not necessarily unitary. We also introduce conformal $d$-vertex algebras, $d$-dimensional analogues of full vertex algebras, and prove that such an algebra is obtained from every system of conformally covariant correlation functions. Finally, for each $d\geq 2$, we construct a family of examples satisfying these axioms, corresponding to generalized free scalar fields. For $d>2$, this family contains both unitary and non-unitary examples.
发表机构
- Interdisciplinary Theoretical and Mathematical Science Program (iTHEMS)（交叉理论与数学科学项目（iTHEMS））
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