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Infrared properties of two-dimensional SU(N)/H nonlinear σ models at nonzero θ angles

Philippe Lecheminant, Yuya Tanizaki, Keisuke Totsuka

SciPost Phys. 18, 183 (2025) · published 10 June 2025

Part of the In Memoriam: Ian Affleck Collection in the In Memoriam Series.

Abstract

A general strategy is proposed to explore the low-energy properties of two-dimensional nonlinear σ models with θ terms. We demonstrate its application to nonlinear σ models with the target space SU(N)/H, which include CPN1, complex Grassmannian manifolds as well as the flag SU(N)/U(1)N1 and SU(N)/SO(N) manifolds. By analyzing the symmetry and its anomaly content, we realize these nonlinear σ models by considering specific deformations of the SU(N)1 conformal field theory. For the flag-manifold SU(N)/U(1)N1 and SU(N)/SO(N) models, those deformations are shown to correspond to the marginal current-current operator with the specific sign which leads to a massless renormalization group flow to the SU(N)1 fixed point. In contrast, a massive regime with a two-fold ground-state degeneracy is found for the CPN1 (N>2) and the Grassmannian nonlinear σ models at θ=π.


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