Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reflection factors and exact g-functions for purely elastic scattering theories

Patrick Dorey, Anna Lishman, Chaiho Rim, Roberto Tateo

TL;DR

This work develops an exact off-critical g-function framework to connect reflection factors of purely elastic boundary theories (ADE and T_r) with perturbed boundary conformal field theories. It constructs minimal and one-parameter families of reflection factors, relates one-parameter deformations to boundary RG flows, and validates the framework through UV g-function checks against coset/CFT data, CPT, and specific models like the three-state Potts model. The results establish a UV/IR dictionary for a broad class of integrable boundary theories and reveal systematic flows between conformal boundary conditions, including symmetry-factor effects in multi-vacua systems. The approach also links boundary reflection data to reductions of sine-Gordon theory, strengthening the physical interpretation of the proposed reflection factors and providing a roadmap for future analyses of boundary bound states and UV/IR couplings.

Abstract

We discuss reflection factors for purely elastic scattering theories and relate them to perturbations of specific conformal boundary conditions, using recent results on exact off-critical g-functions. For the non-unitary cases, we support our conjectures using a relationship with quantum group reductions of the sine-Gordon model. Our results imply the existence of a variety of new flows between conformal boundary conditions, some of them driven by boundary-changing operators.

Reflection factors and exact g-functions for purely elastic scattering theories

TL;DR

This work develops an exact off-critical g-function framework to connect reflection factors of purely elastic boundary theories (ADE and T_r) with perturbed boundary conformal field theories. It constructs minimal and one-parameter families of reflection factors, relates one-parameter deformations to boundary RG flows, and validates the framework through UV g-function checks against coset/CFT data, CPT, and specific models like the three-state Potts model. The results establish a UV/IR dictionary for a broad class of integrable boundary theories and reveal systematic flows between conformal boundary conditions, including symmetry-factor effects in multi-vacua systems. The approach also links boundary reflection data to reductions of sine-Gordon theory, strengthening the physical interpretation of the proposed reflection factors and providing a roadmap for future analyses of boundary bound states and UV/IR couplings.

Abstract

We discuss reflection factors for purely elastic scattering theories and relate them to perturbations of specific conformal boundary conditions, using recent results on exact off-critical g-functions. For the non-unitary cases, we support our conjectures using a relationship with quantum group reductions of the sine-Gordon model. Our results imply the existence of a variety of new flows between conformal boundary conditions, some of them driven by boundary-changing operators.

Paper Structure

This paper contains 18 sections, 182 equations, 1 figure, 8 tables.

Table of Contents

  1. Introduction
  2. The ADET family of purely elastic scattering theories
  3. Minimal reflection factors for purely elastic scattering theories
  4. One-parameter families of reflection factors
  5. Boundary $T_r$ theories as reductions of boundary sine-Gordon
  6. Some aspects of the off-critical $g$-functions
  7. The exact $g$-function for diagonal scattering theories
  8. Models with internal symmetries
  9. Further properties of the exact $g$-function
  10. UV values of the $g$-function
  11. $T_r$
  12. $A_r$, $D_r$ and $E_r$
  13. Checks in conformal perturbation theory
  14. One-parameter families and RG flows
  15. The ultraviolet limit
  16. ...and 3 more sections

Figures (1)

  • Figure 2: The expected RG flow pattern