超对称Renyi熵

纠缠熵在理解场论的信息理论结构和引力的全息性质中有重要的作用。本项目旨在通过系统地研究超对称Renyi纠缠熵的严格计算、基本性质、全息对应和物理应用，以达到更好地理解量子场论的纠缠结构和引力的全息性质的目的。偶数维的共形场论的超对称Renyi熵由共形反常决定，由超对称Renyi熵所满足的信息理论不等式可以得到反常系数的界限。本项目将系统地研究各种共形场论中的此类信息理论不等式所给出的物理约束，从而限制共形理论存在的范围。在AdS/CFT框架下，超对称Renyi熵的全息对偶是一类极端黑洞，本项目计划找出此类对偶的所有例子，并检验对偶关系在计及量子修正时仍然成立。

Entanglement entropy plays important roles in understanding the information theoretic structure of quantum field thoery (QFT) and the holographic aspects of (quantum) gravity. In this project, we plan to study supersymmetric Renyi entropy (SRE), including its exact computation, information theoretic properties, holographic dual and physical applications. In even dimensional conformal field theories, SRE is determined by the conformal anomalies, therefore the inequalies of SRE will give bounds of anomaly coefficients. We will generalize this approach to any dimensions, aiming to find new physical bounds. In AdS/CFT, the holographic dual of SRE is hyperbolic extremal black holes. We plan in this project to find all the duality examples belonging to this class and test the validity of this duality at the level of quantum corrections.