New integrable coset sigma models

Abstract

By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of N copies of a Lie group over some diagonal subgroup and they depend on 3N − 2 free parameters. For N = 1 the corresponding model coincides with the well-known symmetric space sigma model. Starting from the Hamiltonian formulation, we derive the Lagrangian for the N = 2 case and show that it admits a remarkably simple form in terms of the classical ℛ-matrix underlying the integrability of these models. We conjecture that a similar form of the Lagrangian holds for arbitrary N. Specifying our general construction to the case of SU(2) and N = 2, and eliminating one of the parameters, we find a new three-parametric integrable model with the manifold T1,1 as its target space. We further comment on the connection of our results with those existing in the literature.

Integrability vs. RG flow in G × G and G × G/H sigma models

“…We shall also study, in section 3, a gauged analog of the models (1.2) defined on a coset space G × G/H. This theory, which was recently derived from affine Gaudin models in [8], may be viewed as a generalization of the standard G/H symmetric space σ-model, also including WZ terms. For these G × G/H theories to be gauge invariant, the corresponding couplings must satisfy certain linear relations.…”

“…For these G × G/H theories to be gauge invariant, the corresponding couplings must satisfy certain linear relations. In addition, for a gauge invariant model to be classically integrable, the couplings should further satisfy certain polynomial relations [8].…”

“…These are equivalent to adding specific finite counterterms, which may be interpreted as required for preservation of integrability at the quantum level (this is analogous to what was observed on other examples in [4,5]). There are still a few special cases, in particular the integrable T 1,1 model of [8], that are automatically stable under the 2-loop RG flow (see section 3.2). 3 To recall, part of the scheme freedom comes from the prescription of how one treats the antisymmetric 2d tensor ε ab appearing in the B-term in (1.3) in dimensional regularization.…”

“…The model admits as a special limit the conformal GMM model with unequal levels [28][29][30]. Our central observation is that, in the case of the subgroup H in G × G/H being abelian, the gauge invariance conditions of [8] are too restrictive and there is also a second "branch" of gauge invariant theories. This allows a natural generalization of the integrable T 1,1 model of [8] to T 1,q with a general parameter q.…”

“…The aim of this paper is to explore the connection between integrability and the RG flow on some new examples -integrable G × G and G × G/H models that were derived from the affine Gaudin construction [6][7][8]. These models may be viewed as generalizations of the PCM k , 1…”