Intertwining operator in thermal CFTd
Intertwining operator in thermal CFTd
复制标题
热 CFTd 中的交织算子
DOI：
10.1142/s0217751x17500063
复制
发表时间：
2017
影响因子：
1.6
通讯作者：
Satoshi Ohya
中科院分区：
文献类型：
--
作者：
Oikawa T;Satoshi Ohya
共形场论的两点函数是共形代数两个等价表示的缠绕算子的积分核。这种交织算子在共形代数的表示空间中满足一些算子恒等式-交织关系。同时，我们知道散射理论中的S-矩阵算子就是内外粒子的希尔伯特空间之间的交织算子。受这种代数相似性的启发，本文利用Kerimov的纠缠算子方法求解精确S-矩阵的思想，对双曲时空上热CFT的动量空间两点函数提出了一种简单的李代数方法.我们表明，在热CFT上，纠缠关系减少到一定的线性递归关系的两点函数在复杂的动量空间。通过求解这些递推关系，我们得到了任意时空维中纯量原算子超前和滞后两点函数以及正频率和负频率两点Wightman函数的动量空间表示.
It has long been known that two-point functions of conformal field theory (CFT) are nothing but the integral kernels of intertwining operators for two equivalent representations of conformal algebra. Such intertwining operators are known to fulfill some operator identities — the intertwining relations — in the representation space of conformal algebra. Meanwhile, it has been known that the S-matrix operator in scattering theory is nothing but the intertwining operator between the Hilbert spaces of in- and out-particles. Inspired by this algebraic resemblance, in this paper, we develop a simple Lie-algebraic approach to momentum-space two-point functions of thermal CFT living on the hyperbolic space–timeby exploiting the idea of Kerimov’s intertwining operator approach to exact S-matrix. We show that in thermal CFT on, the intertwining relations reduce to certain linear recurrence relations for two-point functions in the complex momentum space. By solving these recurrence relations, we obtain the momentum-space representations of advanced and retarded two-point functions as well as positive- and negative-frequency two-point Wightman functions for a scalar primary operator in arbitrary space–time dimension.