Quantum equivalence ofσmodels related by non-Abelian duality transformations

Abstract

Coupling constant renormalization is investigated in 2 dimensional σ models related by non Abelian duality transformations. In this respect it is shown that in the one loop order of perturbation theory the duals of a one parameter family of models, interpolating between the SU (2) principal model and the O(3) sigma model, exhibit the same behaviour as the original models. For the O(3) model also the two loop equivalence is investigated, and is found to be broken just like in the already known example of the principal model.

Integrable 2d sigma models: Quantum corrections to geometry from RG flow

“…Starting from its form as a deformation of the G/G gWZW model, we will determine the 1-loop correction that comes from integrating out the 2d gauge field A a and confirm that this solves the 2-loop RG equation (1.2), (1.3). Since the non-abelian dual of S 2 is a limit of the λ-model, our result implies that accounting for the determinant contribution in (1.7) should also resolve past problems [41,42,43,44] in verifying that the non-abelian duality commutes with RG flow at the 2-loop level.…”

Non-Abelian duality in the string effective action

“…The only requirement is that the adjoint representation of the isometry Lie algebra is traceless [12,14,18,19]. This relation has been shown to hold at the one-loop level for some particular examples which are, in general, not conformally invariant [17,20,21].…”

Non-abelian T-duality, Ramond fields and coset geometries

“…An alternative approach described in [18,26], is to start directly with the generating functional of the canonical transformation between dual σ-models, apply the above gauge fixing and then calculate the remaining transformations. Finally one sets to zero the components of momenta in the direction of the subgroup since these drop out of the σ-model (3.9) in the coset limit.…”