Sigma models on flags

Ohmori, Kantaro; Seiberg, Nathan; Shao, Shu-Heng

doi:10.21468/SciPostPhys.6.2.017

Sigma models on flags

Journal Article · Sun Feb 03 23:00:00 EST 2019 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.6.2.017· OSTI ID:1493364

Ohmori, Kantaro ^[1]; Seiberg, Nathan ^[1]; ^[1]

Institute for Advanced Study, Princeton University

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) , with a specific focus on the special case U(N)/U(1)^{N} $U (N) / U (1)^{N}$ . These generalize the well-known \mathbb{CP}^{N-1} ${ℂ ℙ}^{N - 1}$ model. The general flag model exhibits several new elements that are not present in the special case of the \mathbb{CP}^{N-1} ${ℂ ℙ}^{N - 1}$ 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 $N_{I}$ and for specific values of the parameters the model is gapless in the IR and is described by an SU(N)_1 $S U (N)_{1}$ WZW model. Some of the techniques we present can also be applied to other cases.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009988

OSTI ID:: 1493364

Journal Information:: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 2 Vol. 6

Publisher:: Stichting SciPostCopyright Statement

Country of Publication:: Country unknown/Code not available

Language:: English

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