$$ T\overline{T} $$ deformation of correlation functions
$$ T\overline{T} $$ deformation of correlation functions
复制标题
$$ Toverline{T} $$相关函数的变形
DOI：
10.1007/jhep12(2019)160
复制
发表时间：
2019
影响因子：
5.4
通讯作者：
J. Cardy
中科院分区：
文献类型：
--
作者：
J. Cardy
摘要
本文研究了二维量子场论中局域场关联函数的演化。
\lambda T\overline{T} $$
λT
不
¯
变形，适当地规则化。我们表明，这可以被看作是在每个领域的演变，在每个无穷小的步骤与一个Dirac字符串连接。变形然后作为整个算子代数的导数，满足莱布尼茨规则。我们推导出一个明确的方程，它允许UV发散的分析，这可能被吸收到一个非本地的场重整化给相关函数是UV有限的所有订单，满足（变形）运营商的产品扩展和Callan-Symanzik方程。我们在变形的CFT的情况下解决了这个问题，表明傅立叶变换的重整化两点函数表现为k
2 +2 k2，其中是它们的IR共形维数。我们详细讨论变形Noether电流，包括能量动量张量，并表明，虽然他们也成为非本地的，适当改进时，他们仍然是有限的，保守的，并满足预期的沃德身份。最后，我们讨论了如何等效的
$$ T\overline{T} $$
不
不
¯
变形到状态依赖的坐标变换出现在该图中。
Abstract
We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the
$$ \lambda T\overline{T} $$
λT
T
¯
deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each field, with a Dirac-like string being attached at each infinitesimal step. The deformation then acts as a derivation on the whole operator algebra, satisfying the Leibniz rule. We derive an explicit equation which allows for the analysis of UV divergences, which may be absorbed into a non-local field renormalization to give correlation functions which are UV finite to all orders, satisfying a (deformed) operator product expansion and a Callan-Symanzik equation. We solve this in the case of a deformed CFT, showing that the Fourier-transformed renormalized two-point functions behave as k
2∆+2λk2, where ∆ is their IR conformal dimension. We discuss in detail deformed Noether currents, including the energy-momentum tensor, and show that, although they also become non-local, when suitably improved they remain finite, conserved and satisfy the expected Ward identities. Finally, we discuss how the equivalence of the
$$ T\overline{T} $$
T
T
¯
deformation to a state-dependent coordinate transformation emerges in this picture.