Sigma Models on Flags

Kantaro Ohmori, Nathan Seiberg, Shu-Heng Shao

Published 2018-09-27Version 1

We study (1+1)-dimensional non-linear sigma models, whose target space is the flag manifold $U(N)\over U(N_1)\times U(N_2)\cdots U(N_m)$. These generalize the well-known $\mathbb{CP}^{N-1}$ model. The general flag model exhibits several new elements that are not present in the special case of the $\mathbb{CP}^{N-1}$ 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.