Conserved Monodromy RTT=TTR Algebra in the Quantum Self-Dual Yang-Mills System

TL;DR

This paper discovers a conserved monodromy matrix in the quantum Self-Dual Yang-Mills system, revealing integrable structures and infinite conserved algebras in a four-dimensional interacting quantum field theory.

Contribution

It introduces a conserved monodromy matrix satisfying RTT=TTR relations and derives infinite quantum nonlocal-charge and Yangian algebras in the SDYM system.

Findings

Existence of conserved monodromy matrix in quantum SDYM

Derivation of infinite quantum nonlocal-charge algebras

Derivation of infinite conserved Yangian algebras

Abstract

We find a conserved monodromy matrix differential operator T in the quantum Self-Dual Yang-Mills (SDYM) system and show that it satisfies the exchange algebra RTT=TTR. From its two infinitesimal forms, we obtain the infinite conserved quantum nonlocal-charge algebras and the infinite conserved Yangian algebras. It is remarkable that such conserved algebras exist in a four-dimensional nontrivial quantum field theory with interactions.