On the Fermionic Quasi-particle Interpretation in Minimal Models of Conformal Field Theory

TL;DR

This paper examines the fermionic quasi-particle interpretation in minimal conformal field theories, confirming its validity only for the Ising model through analysis of eigenstates and integrals of motion.

Contribution

It provides a verification of the fermionic quasi-particle eigenstate conjecture in minimal models, highlighting its limitation to the Ising case.

Findings

Confirmed the conjecture for the Ising model

Showed the conjecture does not hold for other minimal models

Clarified the eigenstate structure in minimal conformal theories

Abstract

The conjecture that the states of the fermionic quasi-particles in minimal conformal field theories are eigenstates of the integrals of motion to certain eigenvalues is checked and shown to be correct only for the Ising model.