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

Abstract

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