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Light-Cone Bootstrap of Higher Point Functions and Wilson Loop Duality
Carlos Bercini1, Vasco Gonçalves1,2, Pedro Vieira1,3
1ICTP South American Institute for Fundamental Research, IFT-UNESP, So Paulo 01140-070, Brazil.
Physical Review Letters
|April 9, 2021
Summary
We explore the conformal bootstrap for gauge theories, constraining operator structures in null polygonal limits. This method precisely determines operator properties in specific non-Abelian conformal theories.
Area of Science:
- Theoretical High Energy Physics
- Quantum Field Theory
- String Theory
Background:
- The conformal bootstrap is a powerful tool for studying quantum field theories.
- Understanding correlation functions is crucial for probing theory dynamics.
- Previous studies focused on simpler cases, leaving higher-point functions less explored.
Purpose of the Study:
- To develop and apply the conformal bootstrap for n>4 point correlation functions.
- To investigate gauge invariant operators in planar non-Abelian conformal gauge theories.
- To constrain operator product expansion (OPE) structure constants.
Main Methods:
- Utilizing the conformal bootstrap approach.
- Analyzing correlation functions of scalar gauge invariant operators near null polygon cusps.
- Employing OPE consistency in the snowflake channel under cyclic transformations.
- Leveraging duality to null polygonal Wilson loops in N=4 theories.
Main Results:
- Strongly constrained OPE structure constants for large spin and polarization operators in general non-Abelian gauge theories.
- Completely fixed these constants in N=4 theories through duality and hexagon analysis.
- Demonstrated the power of bootstrap methods for complex correlation functions.
Conclusions:
- The conformal bootstrap provides a robust framework for constraining quantum field theories.
- This work advances our understanding of higher-point correlation functions in gauge theories.
- The methods developed offer a path to solving strongly coupled field theories.
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