论文标题
在$ t \ overline {t} $下的状态流
On the flow of states under $T\overline{T}$
论文作者
论文摘要
我们从哈密顿的角度研究了二维量子场理论的$ t \叠加{t} $变形，重点介绍了洛伦兹签名中的理论方面。我们的起点是对$ t \ edline {t} $运算符的空间积分的简单重写，这直接暗示了理论的变形能谱。然后，使用此重写，我们得出了变形理论中各种数量的流动方程，例如能量本征态，运算符和相关函数。在平面上，我们发现变形仅具有沿流动的连续规范/Bogoliubov转换的效果。这导致我们定义了一类非本地的“穿着”操作员（包括穿着的压力张量），该操作员满足与未构造理论相同的换向关系。这进一步意味着，如果原始理论是CFT，则变形理论在平面上保留其对称代数，包括共形对称性。在气缸上，$ t \ Overline {t} $变形更加不平淡，但是即使如此，某些穿着的操作员的相关功能也是原始变换的整体变换。最后，我们在ADS/CFT的背景下提出了张量网络的解释。
We study the $T\overline{T}$ deformation of two dimensional quantum field theories from a Hamiltonian point of view, focusing on aspects of the theory in Lorentzian signature. Our starting point is a simple rewriting of the spatial integral of the $T\overline{T}$ operator, which directly implies the deformed energy spectrum of the theory. Using this rewriting, we then derive flow equations for various quantities in the deformed theory, such as energy eigenstates, operators, and correlation functions. On the plane, we find that the deformation merely has the effect of implementing successive canonical/Bogoliubov transformations along the flow. This leads us to define a class of non-local, 'dressed' operators (including a dressed stress tensor) which satisfy the same commutation relations as in the undeformed theory. This further implies that on the plane, the deformed theory retains its symmetry algebra, including conformal symmetry, if the original theory is a CFT. On the cylinder the $T\overline{T}$ deformation is much more non-trivial, but even so, correlation functions of certain dressed operators are integral transforms of the original ones. Finally, we propose a tensor network interpretation of our results in the context of AdS/CFT.
