Boundary Quantum Field Theories with Infinite Resonance States

Abstract

We extend a recent work by Mussardo and Penati on integrable quantum field theories with a single stable particle and an infinite number of unstable resonance states, including the presence of a boundary. The corresponding scattering and reflection amplitudes are expressed in terms of Jacobian elliptic functions, and generalize the ones of the massive thermal Ising model and of the Sinh-Gordon model. In the case of the generalized Ising model we explicitly study the ground state energy and the one-point function of the thermal operator in the short-distance limit, finding an oscillating behaviour related to the fact that the infinite series of boundary resonances does not decouple from the theory even at very short-distance scales. The analysis of the generalized Sinh-Gordon model with boundary reveals an interesting constraint on the analytic structure of the reflection amplitude. The roaming limit procedure which leads to the Ising model, in fact, can be consistently performed only if we admit that the nature of the bulk spectrum uniquely fixes the one of resonance states on the boundary.

arXiv comment18 pages, 11 figures, LATEX file

References in corpus (17)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Boundary energy and boundary states in integrable quantum field theories
• Factorized Scattering in the Presence of Reflecting Boundaries
• Bound State Boundary S-matrix of the sine-Gordon Model
• Form factors of soliton-creating operators in the sine-Gordon model
• Thermodynamic Bethe Ansatz of the Homogeneous Sine-Gordon models
• Integrable Quantum Field Theories with Unstable Particles
• Bosonic-type S-Matrix, Vacuum Instability and CDD Ambiguities
• Semi-classical spectrum of the Homogeneous sine-Gordon theories
• Reflection factors and a two-parameter family of boundary bound states in the sinh-Gordon model
• On Ising Correlation Functions with Boundary Magnetic Field
• New families of flows between two-dimensional conformal field theories
• Form Factors of the Homogeneous Sine-Gordon models
• Integrable boundary conditions for classical sine-Gordon theory
• ${\Phi }^{(2)}$ Perturbations of WZW Model
• A Quantum Field Theory with Infinite Resonance States
• Constructing Infinite Particle Spectra

Cited by in corpus (4)

• The two-boundary sine-Gordon model
• The Massive Klein-Gordon Field Coupled to a Harmonic Oscillator at the Boundary
• A Jacobian generalization of the pseudo Nambu-Goldstone bosons potential
• Wave equations associated to Liouville-type problems: global existence in time and blow up criteria