Guage fields, strings and gravity

1990年代S的超弦对偶革命最引人入胜和最重要的发现是对规范场理论和弦理论之间长期猜想的对偶的具体实现。它断言了四维最大超对称规范理论和特定十维时空几何中的弦理论之间的精确映射。规范场论将永远是物理学的重要组成部分。它们是基本粒子的标准模型的组成部分，描述了粒子物理实验中在目前可获得的能级上看到的现象，其中一些达到了令人难以置信的精度。人们认为，这些规范场可能会有另一种描述为弦理论的想法，这是一个具有深远影响的想法。但在实践层面上，它可以产生新的分析工具，有助于更好地理解规范场理论，并在目前已知技术无法获得的区域中做出定量预测。它已经提供了关于规范理论在强耦合区域行为的相当直观的信息，在强耦合区域，规范理论的非线性很大，而且是常见的技术。微扰理论不能应用。这个研究项目将在形式层面上研究规范场和弦之间的对偶性，以更好地理解它在一个已知的显式例子中的结构，以及在实践层面上，学习如何将其用作分析现实规范理论的量化工具。其他具体项目将使用高度对称的状态来探索ADS/CFT的结构，使用弦理论的可积性和经典解来探索规范理论算符的谱，以及使用格点规范理论的技术来研究矩阵量子力学。

The most fascinating and important discovery of the superstring duality revolution of the 1990's was a concrete realization of the long-conjectured duality between gauge field theory and string theory. It asserts an exact mapping between maximally supersymmetric gauge theory in four dimensions and  string theory in a particular ten-dimensional spacetime geometry.  Gauge field theories will forever be an important part of physics. They are the constituents of the `Standard Model' of elementary particles and describe phenomena seen in particle physics experiments at presently accessible energy scales, some to incredible accuracy.  That these gauge fields might have an alternative description as string theories is an idea with far-reaching consequences.  At a practical level, it could yield new analytical tools which would help to better understand gauge field theories and make quantitative predictions in regimes which are inaccessible to currently known techniques.  It has already provided considerable intuition about the behavior of gauge theories in the strong coupling regime, where their non-linearities are large and the usual technique, perturbation theory cannot be applied.  This research program will study the implications of the duality betweeen gauge fields and strings, both at a formal level to better understand its structure in the one known explicit example, and at a practical level, to learn how to use it as a quantitative tool for the analysis of realistic gauge theories.   Specific projects explore the structure of AdS/CFT using highly symmetric states, the spectra of gauge theory operators using integrability and classical solutions of string theory and studies of matrix quantum mechanics using the techniques of lattice gauge theory.