弦理論與凝態物理對偶

Abstract

AdS/CFT 對偶猜想在弦理論中已經研究了十多年。人們猜想在AdS時空背景下的弦理論與一個在這個AdS時空邊界上的共性場論對偶。在一些特定的極限下，這個對偶成為在一個在AdS時空背景下的弱耦合古典引力理論與一個在這個AdS時空邊界上的強耦合場論的對偶。我們打算把AdS/CFT對偶應用到以下兩種情形：AdS/CMT 和Kerr/CFT. 在AdS/CMT情形下，我門將研究一個標量場在包含電磁場與dilaton粒子的愛因斯坦引力背景下的行為。我們將考慮一些情況，包括不同的dilaton位勢，不同的標量場相互作用，高階曲率，Chern-Simon項和加入D-brane等。根據AdS/CMT對偶，我們將用在這些背景下的引力理論去研究凝態物理中的一些現象，例如超流，超導和量子霍爾效應等。通過跟實驗數據的比照，我們希望能過構造一個實際的AdS/CMT模型。 在Kerr/CFT情形下，我們將研究非極化黑洞的近視界區域。通過對近視界幾何的研究構造Virasoro代數，并計算它的中心荷。我們試圖把先前對極化與準極化Kerr黑洞的工作擴展到一般的非極化黑洞。

The conjecture of AdS/CFT duality has been studied in string theory for more than 10 years. It conjectures that string theory in the AdS spacetime is dual to a conformal field theory on the boundary o the AdS spacetime. In certain limit, it reduces to the duality between a weakly-coupled classical supergravity theory in AdS and a strongly-coupled field theory on its boundary. We are going to apply AdS/CFT duality to two cases, AdS/CMT and Kerr/CFT. In the case of AdS/CMT duality, we will study Einstein-Maxwell-dilaton background coupled to a charged scalar with various dilaton potentials, scalar interactions, higher order curvature term, Chern-Simon term and probe branes, etc. We will use these gravity backgrounds to study some effects in the condensed matter theory, such as superfluity, superconductor and quantum Hall effect. By comparing to the experimental data, we hope to construct a realistic AdS/CMT model. In the case of Kerr/CFT, we will study the near horizon region of non-extreme black holes. We will study its near horizon geometry and construct the Virasoro algebra, then calculate its central charge. We try to extend the previous work of extreme and near-extreme Kerr black hole to the case of non-extreme black hole.