Integrable RG Flows on Topological Defect Lines in 2D Conformal Field Theories

TL;DR

This paper introduces integrable lattice models that realize and interpolate between topological defect lines in 2D conformal field theories, enabling analytical and numerical study of their RG flows and properties.

Contribution

It presents a family of parameter-dependent integrable lattice models based on quantum-inverse scattering, realizing different TDLs and their RG flows in minimal CFTs.

Findings

Constructed explicit defect Hamiltonians and line operators in closed form.

Demonstrated RG flows between different TDLs using Bethe-ansatz and numerical methods.

Connected TDLs with models like the anisotropic Kondo model.

Abstract

Topological defect lines (TDLs) in two-dimensional conformal field theories (CFTs) are standard examples of generalized symmetries in quantum field theory. Integrable lattice incarnations of these TDLs, such as those provided by spin/anyonic chains, provide a crucial playground to investigate their properties, both analytically and numerically. Here, a family of parameter-dependent integrable lattice models is presented, which realize different TDLs in a given CFT as the parameter is varied. These models are based on the general quantum-inverse scattering construction, and involve inhomogeneities of the spectral parameter. Both defect hamiltonians and (defect) line operators are obtained in closed form. By varying the inhomogeneities, renormalization group flows between different TDLs (such as the Verlinde lines associated with the Virasoro primaries $(1,s)$ and $(s,1)$ in diagonal minimal CFTs) are then studied using different aspects of the Bethe-ansatz as well as ab-initio numerical techniques. Relationships with the anisotropic Kondo model as well as its non-Hermitian version are briefly discussed