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Updated: Jul 12, 2025
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Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
Published on: August 18, 2017
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Free Field Realisation of the Chiral Universal Centraliser
Christopher Beem1, Sujay Nair1
1Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG UK.
Annales Henri Poincare
|October 30, 2023
Summary
This study introduces a free field realization for chiral algebras, simplifying complex theories in quantum field theory. This breakthrough clarifies generalized S-duality and offers new insights into Higgs branches and vertex algebras.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Algebraic Geometry
Background:
- The Moore-Tachikawa formalism describes Higgs branches using topological quantum field theory (TQFT).
- The universal centralizer and chiral universal centralizer are key spaces in this formalism.
- Existing work by Kostant established foundational results on the Kostant-Toda lattice.
Purpose of the Study:
- To construct a symplectic embedding from a cover of the Kostant-Toda lattice to the universal centralizer.
- To propose a free field realization of the chiral universal centralizer for any simple group G.
- To develop free field realizations of chiral algebras for specific types of quantum field theories.
Main Methods:
- Construction of an open, symplectic embedding extending Kostant's results.
- Analysis of the Poisson algebraic structure of the universal centralizer.
- Development of free field realizations based on the constructed embedding.
Main Results:
- An explicit free field realization of the chiral universal centralizer for simple groups G is proposed.
- Free field realizations of chiral algebras of class S for genus zero theories with punctures are developed.
- These realizations render generalized S-duality manifest.
Conclusions:
- The proposed free field realizations provide a powerful tool for studying chiral algebras and their dualities.
- The framework is extendable to theories with more punctures, though with increased technical complexity.
- This work deepens the understanding of the relationship between Higgs branches, Coulomb branches, and chiral algebras.
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