Topics in String Theory

超弦理论是基本粒子标准模型与广义相对论在一个与量子力学一致的框架内统一的最有希望的候选者。本文提出的研究计划包括三个主要主题：第一，双环及以上的超弦微扰理论，及其在超重力、有限和异常弦修正中的应用；第二，黑洞在AdS/CFT对应中，着重描述了BPS微观状态的体边界理论；第三，超重力解、开弦速子凝聚和宇宙学场景下的时间依赖弦理论。一些额外的研究课题也在计划中，包括在弦理论背景下引力奇点公式的数值模拟。与数学家一起组织跨学科研讨会涉及到跨学科的方面。更广泛的影响还包括为学生编写教科书。

Superstring theory is the most promising candidate for the unification of the Standard Model of elementary particles with General Relativity in a framework consistent with Quantum Mechanics. The research program being proposed here consists of three major themes: _first, superstring perturbation theory at two-loops and beyond, with applications to string corrections to super-gravity, finiteness, and anomalies; second, black holes in the AdS/CFT correspondence, with emphasis on the bulk description of BPS microstates of the boundary theory; third, time dependent string theory within the context of supergravity solutions, open string tachyon condensation, and cosmological scenarios. A number of additional research topics are also planned including numerical simulations of the formulation of gravitational singularities in the context of string theory. There is an interdisciplinary aspect involved with organizing interdisciplinary workshops with mathematicians. Broader implications also include the writing of a textbook for students.