Boundary Quantum Field Theories with Infinite Resonance States

TL;DR

This paper explores boundary quantum field theories with infinite resonance states, generalizing known models using elliptic functions, and analyzes their ground state energy and boundary effects, revealing oscillatory behaviors and structural constraints.

Contribution

It introduces a new class of boundary quantum field theories with infinite resonances using elliptic functions, extending previous models and analyzing their boundary effects and resonance structures.

Findings

Oscillating behavior in ground state energy and one-point functions.

Boundary resonance states do not decouple at short distances.

Constraints on reflection amplitude structure from the roaming limit.

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.