Abstract

Nonlinear sigma models are field theories that play an important role in many areas of modern mathematical and theoretical physics, ranging from string theory to condensed matter physics. In this talk we focus on the two-dimensional sigma models on the symmetric spaces SO(n)/SO(n−1), traditionally referred to as O(n) symmetric–space sigma models (SSSM). This class is of particular interest in light of its integrability at both the classical and quantum levels. Several deformations of these models are known to preserve integrability (at least classical), with one important example being the Yang–Baxter (YB), or η-deformation, with η serving as the deformation parameter. YB-SSSM has several remarkable properties as a quantum field theory: it is renormalizable with a single running coupling η, and it is asymptotically free. Moreover, by using the duality between O(n) sigma models and generalized Thirring quantum field theories (QFT), one can show that the quantum integrability of the sigma model is preserved whenever the corresponding QFT exhibits factorized scattering. In this talk we will focus on the examples with n = 3 and n = 4, and it will be shown that the latter additionally exhibits a so-called twisted YB-deformation corresponding to a twist of the underlying algebra.