Holography and Integrability in String Theory

我们对将原子核的基本成分（夸克和胶子）结合在一起的力的理解基于一种称为量子色动力学的理论。在非常高的能量下，夸克可以自由移动，我们可以很好地描述正在发生的事情。另一方面，在日常能量下，夸克被限制在一起，我们当前的理论工具和计算技能还远远不能提供系统的良好物理图像。用技术术语来说，我们在短距离处具有渐近自由度，而在远距离处则具有限制性。我们当前的理论工具无法解决最基本的问题，例如质子的质量是多少。为了在这些尺度上理解自然，我们必须开发新的数学工具和更好的物理直觉。对于某些粒子理论，我们正在寻找的工具似乎就在眼前，并且被称为全息性和可积性（即精确可解性）。这些场论还从全息意义上描述了称为弦理论的量子引力理论的动力学。因此，在可积性和全息技术的帮助下，我们离爱因斯坦的引力理论和量子力学的融合更近了一步，这是物理学中最美丽、最重要的开放问题之一。

Our understanding of the force that binds together the fundamental constituents (quarks and gluons) of atomic nuclei is based on a theory called quantum chromodynamics. At very high energies the quarks move freely and we have a good description of what is going on. On the other hand, at everyday energies the quarks are confined together and our current theoretical tools and computational skills are very far from providing a good physical picture of the system. In technical terms, we have asymptotic freedom at short distances and confinement at large distances. The most basic questions such as what is the mass of a proton can not be accessed with our current theoretical tools. To understand nature at these scales we must develop new mathematical tools and better physical intuition. For some particle theories, the tools we were looking for seem to be at hand and go by the name of Holography and Integrability (i.e. exact solvability). These field theories also describe, in an holographic sense, the dynamics of a quantum theory of gravity called string theory. With the help of Integrability and Holography techniques we are thus moving closer to merging Einstein's theory of gravity and quantum mechanics, one of the most beautiful and important open problems in physics.