Non-perturbative Conformal Field Theory in Quantum Gravity and the Laboratory (Exact CFT)

我的建议将探讨非微扰方面的共形场理论（CFTs）与应用程序的高能量和凝聚态系统。在凝聚态物质中，CFTs描述了量子材料，这些材料是当前和未来实验的目标。在高能量下，CFT通过著名的AdS/CFT对偶性提供了唯一已知的量子引力的非微扰描述。然而，这些CFTs通常是强耦合的，因此无法使用费曼图等标准微扰工具进行研究。我的计划是结合联合收割机尖端的非微扰方法，如共形引导，超对称本地化，谐波分析，以回答长期存在的问题，在强耦合物理。这项建议分为两个相关的部分：第一部分。用对偶CFT非微扰地研究量子引力。对于弦和M理论，目标是计算普朗克长度展开中所有阶的引力子散射，并研究这种散射中出现的黑洞状态。对于更高自旋引力的简单情况，我们的目标是将我最近推导的适用于负时空曲率的AdS/CFT推广到与宇宙学相关的正时空曲率情况，并与弦/M理论AdS/CFT联系起来。这条线的输出将通过计算量子引力中的精确物理观测值来实现全息原理的梦想。研究2+1维的量子色动力学，作为代数自旋液体，去限制临界性和分数量子霍尔态之间的过渡的涌现描述。目标是确定这些理论何时是共形的，计算临界指数，验证最近提出的对偶，并找到新的对偶。这条链的输出将预测物理观测值，可以指导正在进行的和未来的实验。由于这些CFTs是双重的更高的自旋引力，链I的输出也将通知链II的研究。

My proposal will explore non-perturbative aspects of conformal field theories (CFTs) with applications to both high energy and condensed matter systems. In condensed matter, CFTs describe quantum materials that are the target of current and future experiments. In high energy, CFTs provide the only known non-perturbative description of quantum gravity via the famous AdS/CFT duality. These CFTs are often strongly coupled, however, so they cannot be studied using standard perturbative tools such as Feynman diagrams. My plan is to combine cutting edge non-perturbative methods such as the conformal bootstrap, supersymmetric localization, and harmonic analysis to answer long standing questions in strongly coupled physics. This proposal is divided into two related strands:Strand I. Non-perturbatively study quantum gravity via the dual CFT. For string and M-theory, the goals are to compute graviton scattering to all orders in the Planck length expansion, and study black hole states that appear in this scattering. For the simpler case of higher spin gravity, the goals are to extend my recent derivation of AdS/CFT, which applies to negative spacetime curvature, to the cosmologically relevant case of positive spacetime curvature, and to connect to string/M-theory AdS/CFT. The outputs of this strand will realize the dream of the holographic principle by computing exact physical observables in quantum gravity.Strand II. Study quantum chromodynamics in 2+1 dimensions as an emergent description of algebraic spin liquids, deconfined criticality, and the transition between fractional quantum hall states. The goals are to determine when these theories are conformal, compute critical exponents, verify recently proposed dualities, and find new dualities. The outputs of this strand will predict physical observables that can guide ongoing and future experiments. Since these CFTs are dual to higher spin gravity, the output of strand I will also inform the research of strand II.