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From Gaudin Integrable Models to d-Dimensional Multipoint Conformal Blocks.

Ilija Burić¹, Sylvain Lacroix^2,3, Jeremy A Mann¹

¹DESY Theory Group, DESY Hamburg, Notkestrasse 85, D-22603 Hamburg, Germany.

Physical Review Letters

|January 29, 2021

Summary

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This study introduces an integrability-based method for multipoint conformal blocks in higher-dimensional conformal field theories. Conformal blocks are found to be eigenfunctions of Gaudin Hamiltonians, enabling their evaluation via differential equations.

Area of Science:

Theoretical Physics
High-Energy Physics
Mathematical Physics

Background:

Conformal field theories (CFTs) are crucial in understanding critical phenomena and quantum gravity.
Multipoint conformal blocks are essential for calculating correlation functions in CFTs.
Higher-dimensional CFTs present unique challenges in block computation.

Purpose of the Study:

To develop a novel, integrability-based approach for computing multipoint conformal blocks.
To establish a connection between conformal blocks and integrable systems.
To provide a systematic method for evaluating these blocks in higher dimensions.

Main Methods:

Utilizing the integrability of Gaudin Hamiltonians.
Identifying conformal blocks as eigenfunctions of these Hamiltonians.

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Deriving a complete set of differential equations for block evaluation.

Main Results:

Conformal blocks for N-point functions are demonstrated to be eigenfunctions of integrable Gaudin Hamiltonians.
A complete set of differential equations for multipoint conformal blocks has been derived.
This approach offers a new pathway for the explicit calculation of conformal blocks.

Conclusions:

The integrability-based approach provides a powerful new tool for studying higher-dimensional CFTs.
The connection to Gaudin Hamiltonians simplifies the evaluation of multipoint conformal blocks.
This work opens avenues for further research in the intersection of integrability and quantum field theory.