Abstract
We compute the anomalous dimension of the single current operator in the case of single and doubly deformed asymmetric λ-models with a general deformation matrix. Our method uses the underlying geometry of the coupling space, as well as an auxiliary group interaction, which completely decouples from the asymmetric model in a specific limit, consistent with the Renormalization Group flow. Our results are valid to all orders in the deformation parameters and leading order to the levels of the underlying current algebras. We specialize our general result to several models of particular interest that have been constructed in the literature and for which these anomalous dimensions were not known.
Highlights
The effective theory (1.1) has an additional remarkable duality-type symmetry, involving the coupling matrix λab, the level k of the Kac-Moody algebra gk and the group element g ∈ G λ → λ−1, k → −k, g → g−1
We compute the anomalous dimension of the single current operator in the case of single and doubly deformed asymmetric λ-models with a general deformation matrix
In this work we presented an easy way to compute exact expressions for the anomalous dimensions of the single current operators for a doubly deformed λ-model with general deformation matrix
Summary
Our starting point is the doubly deformed asymmetric case involving two copies of the semi-simple Lie group G, with different Kac-Moody algebra levels k1, k2, such that the group elements g1 ∈ Gk1, g2 ∈ Gk2. The triple index notation A = (a, a, a) has been used to denote the indices of the first, 2As it has been proved in [8,9,10] and [12] the two flows of (2.1) are decoupled and this limit is valid, with the results for (2.1) corresponding to two copies of the (2.4) ones. For this model we can compute the anomalous dimension of the two composite operators J1+J2− and J1+J3− by using the couplings’ space geometry.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
