A Quantum Field Theory with Infinite Resonance States

TL;DR

This paper introduces an integrable quantum field theory featuring an infinite spectrum of resonance states, with an exact S-matrix expressed via elliptic functions, connecting to conformal field theories and extending the Sinh-Gordon model.

Contribution

It presents a novel integrable QFT with infinite resonance states and derives its exact S-matrix using elliptic functions, also exploring form factors and connections to conformal theories.

Findings

Exact S-matrix expressed with Jacobian elliptic functions

Infinite solutions for form factor equations

Relation to irrational conformal field theories in UV limit

Abstract

We study an integrable quantum field theory of a single stable particle with an infinite number of resonance states. The exact $S$--matrix of the model is expressed in terms of Jacobian elliptic functions which encode the resonance poles inherently. In the limit $l \to 0$, with $l$ the modulus of the Jacobian elliptic function, it reduces to the Sinh--Gordon $S$--matrix. We address the problem of computing the Form Factors of the model by studying their monodromy and recursive equations. These equations turn out to possess infinitely many solutions for any given number of external particles. This infinite spectrum of solutions may be related to the irrational nature of the underlying Conformal Field Theory reached in the ultraviolet limit. We also discuss an elliptic version of the thermal massive Ising model which is obtained by a particular value of the coupling constant.