Implications of conformal invariance in momentum space
Implications of conformal invariance in momentum space
复制标题
DOI：
10.1007/jhep03(2014)111
复制
发表时间：
2013-04
影响因子：
5.4
通讯作者：
A. Bzowski;Paul McFadden;Kostas Skenderis
中科院分区：
文献类型：
--
作者：
A. Bzowski;Paul McFadden;Kostas Skenderis
本文综合分析了应力-能量张量、守恒电流和标量算子的三点函数在一般维度和动量空间中的共形不变性。我们的出发点是一种新颖且非常有效的张量相关器分解方法，它将张量相关器的计算减少到一些标量形式因子的计算。例如，一个守恒的无迹应力-能量张量的最一般的三点函数仅由五个形状因子决定。然后，膨胀和特殊的保角沃德恒等式对这些形状因素施加了额外的条件。特殊的共形Ward恒等式变成了一阶和二阶微分方程的集合，其通解是用包含三个贝塞尔函数积的积分给出的（“3k积分”）。总而言之，相关器在一定常数范围内是完全确定的，与众所周知的位置空间结果一致。在奇维中，三点函数是有限的，不需要进行重整，而在偶维中，则需要进行非平凡的重整。在本文中，我们将自己限制在奇维。对重整的全面分析将在其他地方讨论。
We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (‘triple-K integrals’). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. In odd dimensions 3-point functions are finite without renormalisation while in even dimensions non-trivial renormalisation in required. In this paper we restrict ourselves to odd dimensions. A comprehensive analysis of renormalisation will be discussed elsewhere.