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 two- and 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.
Highlights
Theories go under the name of λ-deformations
It turns out that this corresponds to setting up a large k perturbative expansion of the effective action around the free field point associated with the identity group element
We include all field interaction terms up to sixth order. 1The resulting action will be a two-dimensional quantum field theory with a canonical kinetic term, but in principle one may keep an infinite number of interaction terms involving successively more and more fields
Summary
Our starting point will be he λ-deformed action for an element g of a semi-simple group G given by [4]. It will be useful to parametrize the group element g ∈ G in terms of normal coordinates as g = eitaxa ,. It turns out that we will need the action (2.4) up to O(1/k2) in the large k expansion. The first term of the action (2.4) gives to the specified order in the large-k expansion the action. A definition which will be used in the rest of the paper In this expansion, we have kept the free part properly normalized as well as interactions up to the sixth order. We need to expand H0 to O(1/k2) and read off the corresponding two-form antisymmetric tensor B0 and its contribution to the action. To verify that the same β-function follows from the renormalization of the quartic interaction the coupling g6 is necessary
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