Notes on index of quantum integrability

Abstract

A quantum integrability index was proposed in \cite{KMS}. It systematizes the Goldschmidt and Witten's operator counting argument \cite{GW} by using the conformal symmetry. In this work we compute the quantum integrability indexes for the symmetric coset models $SU(N)/SO(N)$ and $SO(2N)/SO(N)\times SO(N)$. The indexes of these theories are all non-positive except for the case of $SO(4)/SO(2)\times SO(2)$. Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the ${\mathbb{CP}}^N$ model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well.

20 pages

References in corpus (5)

• Operator bases, $S$-matrices, and their partition functions
• On the integrability of two-dimensional models with U(1)xSU(N) symmetry
• Integrable properties of sigma-models with non-symmetric target spaces
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• An Index for Quantum Integrability