Large Spin Perturbation Theory for Conformal Field Theories

Area of Science:

• Theoretical Physics
• Quantum Field Theory

Background:

• Conformal Field Theories (CFTs) are crucial in understanding critical phenomena and quantum gravity.
• Analyzing CFTs often involves studying four-point correlators and operator content.
• Large twist degeneracy presents a specific challenge in CFT analysis.

Purpose of the Study:

• To develop a novel method for analyzing CFTs at points of large twist degeneracy.
• To introduce and define twist conformal blocks.
• To provide a systematic approach for decomposing four-point correlators and computing spectra.

Main Methods:

• Introduction of twist conformal blocks as eigenfunctions of quartic operators.
• Systematic construction of decomposed twist conformal blocks when degeneracy is lifted.
• Application of the method to four-point correlators in various CFTs.

Main Results:

• Twist conformal blocks encode the contribution of operator towers to four-point correlators.
• Decomposition of blocks provides a systematic way to handle broken degeneracy.
• Crossing symmetry is transformed into an algebraic problem.

Conclusions:

• The developed method is broadly applicable to diverse CFTs in any dimension.
• The technique allows for systematic computation of spectra, as demonstrated around generalized free fields.
• This approach offers a powerful tool for studying CFTs with broken higher spin symmetry.