论文标题
较高维度的CFTS为2D - 符合性的拓扑结构理论
Higher dimensional CFTs as 2D conformally-equivariant topological field theories
论文作者
论文摘要
四维CFT中主要字段的两个和三分函数具有简单的时空依赖，从组合结构中分解出来，该结构列举了磁场并给出了它们的耦合。这导致了具有$ SO（4,2）$均衡的两维拓扑场理论的提出，该理论被认为等同于更高维度的保形场理论。我们在自由标量场的最简单设置中审查了此CFT4/TFT2构造，从无限的尺寸$ SO（4,2）$ Equivariant代数为具有有限尺寸的子空间的无限尺寸$（4,2）$ so（4,2）$ so（4,2）$ so（4,2）$ so（4,2），在固定缩放尺寸的情况下。 CFT4的交叉对称性与代数的关联有关。然后，通过使用变形的副产品来扩展该结构以描述扰动CFT4。在Wilson-Fisher CFT的激励下，我们概述了u（so（$ d $，2））非整数$ d $的u（so（$ d $，2））的构建，就图代数及其表示形式而言。
Two and three-point functions of primary fields in four dimensional CFT have a simple space-time dependences factored out from the combinatoric structure which enumerates the fields and gives their couplings. This has led to the formulation of two dimensional topological field theories with $so(4,2)$ equivariance which are conjectured to be equivalent to higher dimensional conformal field theories. We review this CFT4/TFT2 construction in the simplest possible setting of a free scalar field, which gives an algebraic construction of the correlators in terms of an infinite dimensional $so(4,2)$ equivariant algebra with finite dimensional subspaces at fixed scaling dimension. Crossing symmetry of the CFT4 is related to associativity of the algebra. This construction is then extended to describe perturbative CFT4, by making use of deformed co-products. Motivated by the Wilson-Fisher CFT we outline the construction of U(so($d$,2)) equivariant TFT2 for non-integer $d$, in terms of diagram algebras and their representations.
