Quantum Groups as Global Symmetries II. Coulomb Gas Construction

TL;DR

This paper constructs and analyzes a conformal field theory with quantum group symmetry using Coulomb gas techniques, providing explicit correlation functions and operator product expansion coefficients, and exploring the role of quantum groups in minimal models.

Contribution

It introduces a Coulomb gas construction for a quantum group symmetric conformal field theory, including explicit correlation functions and OPE coefficients, and clarifies the role of quantum groups in non-chiral operators and minimal models.

Findings

Explicit correlation functions and OPE coefficients derived.

Quantum group symmetry verified in correlation functions.

Insights into defects and quantum groups in minimal models.

Abstract

We study a conformal field theory that arises in the infinite-volume limit of a spin chain with $U_q(sl_2)$ global symmetry. Most operators in the theory are defect-ending operators which allows $U_q(sl_2)$ symmetry transformations to act on them in a consistent way. We use Coulomb gas techniques to construct correlation functions and compute all OPE coefficients of the model, as well as to prove that the properties imposed by the quantum group symmetry are indeed satisfied by the correlation functions. In particular, we treat the non-chiral operators present in the theory. Free boson realization elucidates the origin of the defects attached to the operators. We also comment on the role of quantum group in generalized minimal models.