变形的约化密度矩阵及其全息对偶的研究

共形场子区域的Deformed约化密度矩阵是一个非局域共形不变量，它是通过对Modular哈密顿量和OPE块(block)作指数映射得到，被认为包含了共形场的丰富细节信息。有趣的是，它的真空期望值的对数可能表现出和几何纠缠熵类似的面积律。在这个项目中，我们计划研究共形场论中Deformed约化密度矩阵的期望值。这个期望值的对数是一般Y-型连通关联函数的生成函数，我们期望能够从它们读取能标无关的信息。我们将通过对一般Y-型连通关联函数的解析延拓仔细探讨各种UV/IR的关系。最后，我们将在引力对偶位形中计算测地线Witten图，从而给出对一般Y-型连通关联函数的全息描述。

Deformed reduced density matrix of a subregion is a non-local invariant which has been shown to encode rich details of conformal field theory.It is generated by exponential map of modular Hamiltonian and OPE blocks.Interestingly, the logarithm of its vacuum expectation value may present similar area law as geometric entanglement entropy.In this program, we propose to study expectation value of deformed reduced density matrix in conformal field theory.Its logarithm is a generator of so-called Y-type connected correlation functions.We expect to read cutoff independent details from these correlators. We will discuss varies UV/IR relations by analytic continuation of Y-type connected correlation functions.We will present a holographic description for general Y-type connected correlation function by calculating geodesic Witten diagram in the bulk.