Quantum aspects of doubly deformed CFTs

Abstract

We study quantum aspects of the recently constructed doubly lambda-deformed sigma-models representing the effective action of two WZW models interacting via current bilinears. We show that although the exact beta-functions and current anomalous dimensions are identical to those of the lambda-deformed models, this is not true for the anomalous dimensions of generic primary field operators in accordance with the fact that the two models differ drastically. Our proofs involve CFT arguments, as well as effective sigma-model action and gravity calculations.Comment: 1+26 pages, Late

Integrable flows between exact CFTs

“…However, the fact that in (2.17) the defining CFT theories, that is the two WZW models, are decoupled, implies that there is no mixing between the two deformation parameters. The arguments in favour of that are identical to those presented for the equal level case in [45]. In fact the beta-function found by CFT perturbative methods in [42] and in [43] is…”

“…2 For the equal level case, this approach was taken in [45] resulting into a complete agreement with the CFT results. In our case we will use the action (2.18) in order to compute the one loop RG flow equations [54][55][56][57][58][59][60] …”

“…Self-interacting terms of the form appearing in (1.1) and (1.2) are absent. The anomalous dimensions of current and primaries in this theory were computed using CFT techniques and symmetry arguments in [45]. It turns out that the effective action corresponding to (1.3) is canonically equivalent [46] to the effective action of the sum of two models of the form (1.1).…”

“…The argument goes as the one in [45]. All correlation functions involving the operators of the set O = {J a 1+ , J a 2− , J a 1+ J b 2− , · · · } or any other composite operator built from them can be calculated as if the vertex proportional to λ 2 in (2.17) was absent.…”

“…This fact implies that (2.18) should have on-shell chiral and anti-chiral currents. Following a procedure parallel to that in [45] we find that the equations of motion from varying the groups elements can be cast in the form…”