Currents, Charges, and Canonical Structure of Pseudodual Chiral Models

TL;DR

This paper analyzes the Pseudodual Chiral Model (PCM) as a two-dimensional theory with an infinite tower of conservation laws that nevertheless permits particle production, contrasting it with the conventional chiral model (CM). It develops a canonical framework linking CM to an equivalent dual sigma model (DSM) with nontrivial metric and torsion, and shows this map does not connect to the PCM, thereby clarifying inequivalence. The PCM’s symmetry structure is clarified by transmuting CM currents into PCM currents ($Z_\mu$, $R_\mu$) and by constructing a refined nonlocal-current algorithm, including a master-current formalism and a seeded construction that yields genuinely nonlocal charges at higher orders. At the classical level, the full nonlocal charge hierarchy is shown to be conserved and to leave the Hamiltonian and momentum invariant, with a quantum-formulation described via a transformation functional linking eigenfunctionals of the two theories. Overall, the work deepens understanding of integrable 2D field theories with torsion, revealing how infinite nonlocal symmetries can coexist with particle production and providing a detailed canonical map between related sigma-models.

Abstract

We discuss the pseudodual chiral model to illustrate a class of two-dimensional theories which have an infinite number of conservation laws but allow particle production, at variance with naive expectations. We describe the symmetries of the pseudodual model, both local and nonlocal, as transmutations of the symmetries of the usual chiral model. We refine the conventional algorithm to more efficiently produce the nonlocal symmetries of the model, and we discuss the complete local current algebra for the pseudodual theory. We also exhibit the canonical transformation which connects the usual chiral model to its fully equivalent dual, further distinguishing the pseudodual theory.