Field theory and λ-deformations: Expanding around the identity

Abstract

We explore the structure of the λ-deformed σ-model action by setting up a perturbative expansion around the free field point corresponding to the identity group element. We include all field interaction terms up to sixth order. We compute the twoand three-point functions of current and primary field operators, their anomalous dimensions as well as the β-function for the λ-parameter. Our results are in complete agreement with those obtained previously using gravitational and/or CFT perturbative methods in conjunction with the non-perturbative symmetry, as well as with those obtained using methods exploiting the geometry defined in the space of couplings. The advantage of this approach is that all deformation effects are already encoded in the couplings of the interaction vertices and in the λ-dressed operators.

An exact symmetry in λ-deformed CFTs

“…This approach seems to be the most promising way to make progress in this direction since attempting to use the gravitational approach in obtaining loop-corrections higher than two is really cumbersome. Another promising approach could be to use the free field expansion of the λ-deformed action in [38] and study using standard field theoretical methods the renormalization of the interaction vertices. An advantage of this approach is that all the dependence on the deformation parameter λ is already encoded in the vertices.…”

“…This is due to the choice of the parameter d 0 = − 1 /2 in (3.7) as it has been already noted. Such terms cannot appear, as it can be seen from a free field expansion around the identity group element [38].…”

A free field perspective of λ-deformed coset CFT’s

“…In this section we use the field theory action (2.16) in order to compute the β-function for the deformation parameter λ. The analogous computation for the group case was performed in [26]. We will find precisely the result of [14] obtained by gravitational methods.…”

“…In this section the interacting field theory corresponding to the λ-deformed coset CFT for SU(2)/U(1) will be constructed. Our approach follows in spirit that of [26]. In that work the interacting theory, based on free fields, for the isotropic single λ-deformed σ-model deformation of the WZW model CFT was constructed.…”

“…Recently a new purely field theoretic approach to the study of λ-deformed theories was initiated in [26]. This method was applied to the isotropic case having a single coupling λ.…”