Dual generalizations of sine-Gordon field theory and integrability submanifolds in parameter space

TL;DR

This paper explores dual relationships in two-dimensional quantum field theories using non-local conserved charges, identifying integrability submanifolds and connecting to conformal field theories with parametrized central charges.

Contribution

It introduces dual generalizations of sine-Gordon theories, characterizes integrability submanifolds in parameter space, and links these to conformal field theories through model truncation.

Findings

Affine Toda theories form integrability submanifolds.

Truncation yields conformal field theories in extended complex space.

A parametrized central charge is computed based on projection choices.

Abstract

The dual relationship between two n-1 parameter families of quantum field theories based on extended complex numbers is investigated in two dimensions. The non-local conserved charges approach is used. The lowest rank affine Toda field theories are generated and identified as integrability submanifolds in parameter space. A truncation of the model leads to a conformal field theory in extended complex space. Depending on the projection over usual complex space chosen, a parametrized central charge is calculated.