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

我的提议将探索共形场理论(CFT)的非微扰方面，并将其应用于高能和凝聚态系统。在凝聚态中，CFT描述了当前和未来实验的目标量子材料。在高能情况下，CFT通过著名的ADS/CFT二象性提供了唯一已知的量子引力的非微扰描述。然而，这些CFT通常是强耦合的，因此不能使用费曼图等标准微扰工具来研究它们。我的计划是结合尖端的非微扰方法，如共形自举、超对称定域化和调和分析，来回答强耦合物理中长期存在的问题。这一提议分为两个相关的部分：部分I。通过双CFT非微扰地研究量子引力。对于弦理论和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，并研究在这种散射中出现的黑洞状态。对于更简单的较高自旋引力的情况，目标是将我最近推导的ADS/CFT推广到与宇宙学相关的正时空曲率的情况，并连接到弦/M理论ADS/CFT。这条链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。链II.研究2+1维的量子色动力学，作为代数自旋液体、去受限临界性和分数量子霍尔态之间跃迁的紧急描述。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性，并找到新的对偶性。这条链的输出将预测可以指导正在进行的和未来的实验的物理可观测性。由于这些CFT对更高的自旋重力是双重的，因此链I的输出也将为链II的研究提供信息。

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.