共形块Farey尾
A conformal block Farey tail
摘要：
我们研究了交叉对称性对CFT关联函数的约束。四点共形块自然地被视为上半平面上的函数，交叉对称通过PSL（2，Z）模变换作用于其上。这使得我们可以通过在PSL（2，Z）上求平均值，从给定的共形块中构造出一个唯一的交叉对称函数。在某些二维CFTs中，关联函数精确地等于有限数量的光态的贡献的模平均。例如，在二维伊辛和三临界伊辛模型CFTs中，相同算子的关联函数等于Virasoro真空块的PSL（2，Z）平均值;这根据中心荷唯一地确定了3个点函数系数。CFT 2中PSL（2，Z）上的和具有自然的AdS 3解释，作为半经典鞍点上的和，其描述了粒子沿着本体中的有理缠结传播。我们证明了这一点明确的关联函数的某些沉重的运营商，在那里我们计算全息的半经典共形块与沉重的内部运营商。
英文摘要：
We investigate the constraints of crossing symmetry on CFT correlation functions. Four point conformal blocks are naturally viewed as functions on the upper-half plane, on which crossing symmetry acts by PSL(2,Z) modular transformations. This allows us to construct a unique, crossing symmetric function out of a given conformal block by averaging over PSL(2,Z). In some two dimensional CFTs the correlation functions are precisely equal to the modular average of the contributions of a finite number of light states. For example, in the two dimensional Ising and tri-critical Ising model CFTs, the correlation functions of identical operators are equal to the PSL(2,Z) average of the Virasoro vacuum block; this determines the 3 point function coefficients uniquely in terms of the central charge. The sum over PSL(2,Z) in CFT2 has a natural AdS3 interpretation as a sum over semi-classical saddle points, which describe particles propagating along rational tangles in the bulk. We demonstrate this explicitly for the correlation function of certain heavy operators, where we compute holographically the semi-classical conformal block with a heavy internal operator.
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