AI 中文总结
该研究提出复积分围道上PT-对称标量场论的非微扰解析张量网络表述，推导二维负四次耦合下初始张量解析形式，还证明另一复围道格点配分函数与厄米理论延拓实部的精确有限体积关系。
AI 中文摘要
我们提出了一种定义在复积分围道上的$\u003cspan style="font-style: italic;"\u003ePT\u003c/span\u003e$-对称标量场论的非微扰解析张量网络表述。将该表述应用于负四次耦合下的二维$\u003cspan style="font-style: italic;"\u003ePT\u003c/span\u003e$-对称$\u003cspan style="font-style: italic;"\u003eϕ\u003c/span\u003e^4$理论，我们推导了初始张量的显式解析表达式，并证明其分量根据张量指标和的奇偶性划分为偶扇区与奇扇区。我们进一步在另一种复围道上构建该理论，并在任意维度下解析证明：该围道上定义的格点配分函数，与厄米格点$\u003cspan style="font-style: italic;"\u003eϕ\u003c/span\u003e^4$配分函数解析延拓至负四次耦合后的实部之间，存在精确的有限体积关系。
英文摘要
We develop a non-perturbative analytic tensor network formulation of $\mathcal{PT}$-symmetric scalar field theories defined on complex integration contours. Applying this formulation to the two-dimensional $\mathcal{PT}$-symmetric $ϕ^4$ theory at negative quartic coupling, we derive an explicit analytic expression for the initial tensor and show that its components separate into even and odd sectors according to the parity of the sum of the tensor indices. We further formulate the theory on an alternative complex contour and analytically establish, in arbitrary dimensions, an exact finite-volume relation between the lattice partition function defined on this contour and the real part of the analytic continuation of the Hermitian lattice $ϕ^4$ partition function to negative quartic coupling.
Comments33 pages, 2 figures
