SciPost Phys. 6, 017 (2019) ·
published 4 February 2019

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We study (1+1)dimensional nonlinear sigma models whose target space is the
flag manifold $U(N)\over U(N_1)\times U(N_2)\cdots U(N_m)$, with a specific
focus on the special case $U(N)/U(1)^{N}$. These generalize the wellknown
$\mathbb{CP}^{N1}$ model. The general flag model exhibits several new elements
that are not present in the special case of the $\mathbb{CP}^{N1}$ model. It
depends on more parameters, its global symmetry can be larger, and its 't Hooft
anomalies can be more subtle. Our discussion based on symmetry and anomaly
suggests that for certain choices of the integers $N_I$ and for specific values
of the parameters the model is gapless in the IR and is described by an
$SU(N)_1$ WZW model. Some of the techniques we present can also be applied to
other cases.
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