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arXiv 1907.03394hep-th
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关联函数的$T\bar T$变形

$T\bar T$ deformation of correlation functions

John Cardy

备注：
25 pages, 2 figures. v2: version accepted for publication: absence of power law divergences clarified
发表信息：
J. High Energ. Phys. (2019) 2019: 160
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摘要：

研究了二维量子场论中局域场的关联函数在适当正则化的$λT\bar T$形变下的演化。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局域场重整化给关联函数这是UV有限的所有订单，满足（变形）算子乘积展开和Callan-Symanzik方程。我们解决这个问题的情况下，变形的CFT，傅立叶变换重整化两点函数的行为$k^{2Δ+2λk^2}$，其中$Δ$是他们的IR共形维数。我们详细讨论变形诺特电流，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，并满足预期的沃德恒等式。最后，我们讨论了如何等价的$T\bar T$变形的状态相关的坐标变换出现在这个图片。

英文摘要：

We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the $λT\bar T$ 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 $k^{2Δ+2λk^2}$, where $Δ$ 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 $T\bar T$ deformation to a state-dependent coordinate transformation emerges in this picture.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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