Dynamical decoupling and Kac-Moody current representation in multicomponent integrable systems

TL;DR

This paper explores the conformal invariance of multicomponent integrable systems, linking their response to curvature with Kac-Moody algebra representations and characterizing dynamical decoupling through associated conductivities.

Contribution

It reveals the connection between the dressed charge matrix and Kac-Moody algebra generators, providing a new perspective on dynamical decoupling in integrable systems.

Findings

Dressed charge matrix elements are transition matrix elements of Kac-Moody algebra generators.

Dynamical decoupling is characterized by conductivities related to Cartan currents.

Conformal invariance is analyzed via response to curvature in multicomponent systems.

Abstract

The conformal invariant character of $\nu$-multicomponent integrable systems (with $\nu$ branches of gapless excitations) is described from the point of view of the response to curvature of the two-dimensional space. The $\nu\times\nu$ elements of the dressed charge matrix are shown to be transition matrix elements of the zero ($\mu =0$) components of the diagonal generators of $\nu$ independent Kac-Moody algebras (Cartan currents). The dynamical decoupling which occurs in these systems is characterized in terms of the conductivities associated with the $\mu = 1$ components of the Cartan currents.