Abstract
Abstract
A quantum integrability index was proposed in Komatsu et al (2019 SciPost Phys.
7 065). It systematizes the Goldschmidt and Witten’s operator counting argument (Goldschmidt and Witten 1980 Phys. Lett. B 91 392) 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
(
2
N
)
/
SO
(
N
)
×
SO
(
N
)
. The indexes of these theories are all non-positive except for the case of
SO
(
4
)
/
SO
(
2
)
×
SO
(
2
)
. Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the
CP
N
model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well.
Subject
Physics and Astronomy (miscellaneous)