在最近的幾年中，關於全像原理的進展上有兩個重要的成果，其中之一是關於近極端黑洞之對偶共形場論的描述，在這方面主要的起始點是針對Kerr黑洞，而我們成功地將這方面的結果推廣至Reissner-Nordstrom (RN) 黑洞。其中對偶共形場論的中心核 (central charge) 可以經由時空的漸近對稱群或者近視界幾何的二維有效作用量裡的邊界能動張量中確認出來。對於近極端黑洞時的全像對偶的有效性，也已經由核對黑洞時空中的超輻射散射 (superradiant scattering) 振幅與共形場論中的特定的算符在特定的熱狀態下的兩點函數 (two point function) 來驗證。為了進一步加深我們對全像原理的理解，一個重要的課題便是將所有驗證提升至更普適的條件並推廣至更一般的黑洞，例如高維黑洞等。另一重要成果是著重於現象學的應用方面，從特定研究的物理模型中，例如凝態物理或高溫超導等，確定其場論的描述，再構造出對偶的重力理論的時空解，透過全像原理，我們可以處理在場論中非常困難的強偶合現象，目前的相關計算和實驗結果吻合。因此全像原理提供了一個很有用的方法去分析臨界現象的非微擾行為，將可有廣泛應用。我們在全像原理的相關發展有深入的研究，並已有初步良好的成果，我們將更進一步的推廣並提升我們的成果，並考慮相關的應用。當然我們也會持續先前的研究方向考慮具有高曲率修正的黑洞。 In the past years, there are two important achievements in the development of the holographic principle. One is the dual conformal field theory (CFT) description for the near extremal black holes. The main focus was on the Kerr black holes and we have generalized the results to the Reissner-Nordstrom (RN) black holes. The central charge of dual CFT can be identified from the asymptotic symmetry group of spacetime or from the properties of boundary stress tensor of 2D effective action associated to the near horizon geometry. Furthermore, the validity of holographic duality for the near extremal black holes can be verified by comparing the superradiant scattering amplitude from gravity side and the corresponding two point function of a specified operator on a specified thermal state from CFT side. In order to deep our understanding of holographic principle, an essential subject is to improve the supported evidences and to generalize the results to more general black hole such as in higher dimensions. The other development spotlights the phenomenological applications by constructing gravity solutions which are holographically dual to theoretical field theories of certain interesting physical models such as condensed matter physics, superconductor etc. By using the holographic duality, it is possible to compute the strong coupled phenomena which are difficult problems in the field theory side. For particular models, the holographic results match pretty well with the experimental observations. Thus the holographic duality provides a useful tool to analysis the critical point physics in strong coupled regions. We have intensive study on both developments of holographic duality and already made desirable progress. We are going to investigate on this topic. Moreover, we will continue our investigation on the black holes with higher curvature corrections. 研究期間：9908 ~ 10007
