Dualised σ-models at the two-loop order

Abstract

We adress ourselves the question of the quantum equivalence of non abelian dualised σ-models on the simple example of the T-dualised SU (2) σ-model. This theory is classically canonically equivalent to the standard chiral SU (2) σ-model. It is known that the equivalence also holds at the first order in perturbations with the same β functions. However, this model has been claimed to be non-renormalisable at the two-loop order. The aim of the present work is the proof that it is -at least up to this order -still possible to define a correct quantum theory. Its target space metric being only modified in a finite manner, all divergences are reabsorbed into coupling and fields (infinite) renormalisations.

Integrable 2d sigma models: Quantum corrections to geometry from RG flow

“…Starting from its form as a deformation of the G/G gWZW model, we will determine the 1-loop correction that comes from integrating out the 2d gauge field A a and confirm that this solves the 2-loop RG equation (1.2), (1.3). Since the non-abelian dual of S 2 is a limit of the λ-model, our result implies that accounting for the determinant contribution in (1.7) should also resolve past problems [41,42,43,44] in verifying that the non-abelian duality commutes with RG flow at the 2-loop level.…”

“…In this way, we have identified how earlier problems checking NAD at 2-loop level [41,42,43,44] should be resolved in general. In particular, as for abelian T-duality, NAD (properly modified by quantum α corrections) should also be a symmetry of the σ-model β-functions or the string effective action to all orders in α .…”

Renormalization and asymptotic safety in truncated quantum Einstein gravity

“…I thank P. Forgács for pointing this out. A similar concept of recovering renormalizability by finite quantum deformations was recently employed in the context of T-duality[48]; see also[49].…”

One-loop renormalizability of all 2-dimensional Poisson–Lie σ-models

“…The problem of higher loop corrections to the Poisson-Lie T-duality appears to be more tricky than in the case of the Abelian or traditional non-Abelian T-duality. Of course, one problem to cope with is the fact that a finite one-loop renormalization can change the twoloops divergences [17]. But there is also a structural aspect of the thing: we expect that the two-loops effective action of the model should not probably have the same structure as the classical action (3).…”