Topics in String Theory

超弦理论是将基本粒子标准模型与广义相对论统一在一个与量子力学一致的框架中的最有希望的候选者。本文提出的研究计划包括三大主题：第一，双圈及以上超弦微扰理论，应用于超引力、有限性和反常的弦修正;第二，AdS/CFT对应中的黑洞，重点是边界理论BPS微观态的体描述;第三，在超引力解、开弦快子凝聚和宇宙学情景的背景下的时间相关弦理论。一些额外的研究课题也计划，包括数值模拟的制定引力奇点的背景下，弦理论。有一个跨学科的方面涉及组织跨学科的研讨会与数学家。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.