愛因斯坦-馬克士威-純量系統在強關聯問題的全像應用

Abstract

全像理論是近二十年最重要的理論之一，其提供一個嶄新的觀點，描述了空間內部所包含的資訊可以與空間邊界上涵蓋的資訊量有一對應關係。從現象學的角度，愛因斯坦-馬克士威-純量系統是非常一般性的系統；另一方面，愛因斯坦-馬克士威-純量系統的型式也是超弦理論在低能極限下退化成超引力理論中的特例。

在此篇論文之中，我們系統性的計算出愛因斯坦-馬克士威-純量系統內含黑洞結構的高維度時空解析解。藉由解析解的明顯表達式，可以更充分的掌握物理量的變化，方便探討內部結構的深層意義。例如，量子色動力學中的聲速以及色禁閉問題、凝體理論的金屬絕緣體相變，以及糾纏熵與黑洞熵的關係等等。

Holographic theory is one of the most important theories in last two decades. It delivers a whole new aspect to make a bridge between a space-time and its boundary and claims that the information involves in the bulk are equivalent to the amounts where the boundary enclosed. From the phenomenology point of view, Einstein-Maxwell-scalar is a very general system. On the other hand, we can also derive the EMS form from supergravity by taking the low energy limit of the superstring theory. Therefore, it is worth to understand the EMS system not only in phenomenology but also has theoretical importance. In this thesis, I analytically derive a higher dimensional space-time blackening solutions in Einstein-Maxwell-scalar system systematically. By studying the analytic black hole solution, I can control the changes of physical quantities and understand physical inside within the structures, such as speed of sound and confinement phase transition in QCD, metal/insulator phase transition and also the entanglement entropy, and so on and so forth.