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

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.