Guage fields, strings and gravity

20世纪90年代超弦对偶性革命中最引人入胜和最重要的发现是规范场理论和弦理论之间长期猜想的对偶性的具体实现。它断言四维最大超对称规范理论与特定十维时空几何中的弦理论之间存在精确映射。规范场理论将永远是物理学的重要组成部分。它们是基本粒子“标准模型”的组成部分，描述了在目前可获得的能量尺度下粒子物理实验中看到的现象，其中一些达到了令人难以置信的精度。这些规范场可能有另一种描述，如弦理论，这是一个具有深远影响的想法。在实际层面上，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达到的制度中进行定量预测。它已经对规范理论在强耦合状态下的行为提供了相当直观的认识，在强耦合状态下，规范理论的非线性很大，通常的技术，微扰理论不能应用。这个研究项目将研究规范域和弦之间的对偶性的含义，既在形式层面上更好地理解它在一个已知的明确例子中的结构，也在实践层面上，学习如何将其用作分析现实规范理论的定量工具。具体项目探索AdS/CFT使用高度对称态的结构，使用可积性和弦理论的经典解的规范理论算子的谱，以及使用晶格规范理论技术的矩阵量子力学研究。

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.