Duality-invariant class of two-dimensional field theories

Abstract

We construct a new class of two-dimensional field theories with target spaces that are finite multiparameter deformations of the usual coset G/H-spaces. They arise naturally, when certain models, related by Poisson-Lie T-duality, develop a local gauge invariance at specific points of their classical moduli space. We show that canonical equivalences in this context can be formulated in loop space in terms of parafermionic-type algebras with a central extension. We find that the corresponding generating functionals are non-polynomial in the derivatives of the fields with respect to the space-like variable. After constructing models with three- and two-dimensional targets, we study renormalization group flows in this context. In the ultraviolet, in some cases, the target space of the theory reduces to a coset space or there is a fixed point where the theory becomes free

Poisson-Lie duals of the η deformed symmetric space sigma model

“…understood as an operator equation acting on g. In appendix A (see also [36]) we show that this condition is satisfied if the components of B 0 solve…”

“…The claim of duality has been demonstrated for various low-dimensional examples in [16,35] using results of [36]. Furthermore, starting from a certain first-order action on a Drinfel'd double [37,38], which generalises the duality-invariant action of [39,40] underlying abelian duality, it has been proven for the deformation of the principal chiral model [41].…”

“…. , dim G − dim H. The operator E 0 :g → g written in the {U A ,Ũ A } basis can be written in block form 46) whereĀ :h → h. Following the construction of [36], we are interested in the limit where the number of fields in the original model is reduced by dim H. For this purpose a parameter ǫ is introduced 47) and as ǫ → 0, under some mild assumptions outlined in [36], the model develops a local gauge invariance. This gauge invariance also appears in the first-order action on the Drinfel'd double and hence we would expect this to also be the case for the various Poisson-Lie dual models.…”

“…Let us give a brief overview of the η deformed principal chiral model [10,11]. The principal chiral model for the group-valued field g ∈ G is defined by the action 36) where, as before, κ denotes the Killing form on g. As the terminology suggests, this action is invariant under both the left and right action of G. Furthermore, it is possible to demonstrate that this model admits a Lax pair, and is therefore classically integrable.…”

“…The backgrounds for cases (i) and (ii) were constructed in [36,42] for a matrix E 0 depending on two parameters. In [16] it was shown that in the special case 57) in the ǫ → 0 limit, these backgrounds correspond to those of the η and λ * deformations respectively.…”