We invent a method that exploits the geometry in the space of couplings and the known all-loop effective action, in order to calculate the exact in the couplings anomalous dimensions of composite operators for a wide class of integrable σ-models. These involve both self and mutually interacting current algebra theories. We work out the details for important classes of such operators. In particular, we consider the operators built solely from an arbitrary number of currents of the same chirality, the composite operators which factorize into a chiral and an anti-chiral part, as well as those made up of three currents of mixed chirality. Remarkably enough, the anomalous dimensions of the former two sets of operators turn out to vanish. In our approach, loop computations are completely avoided.
By employing CFT techniques, we show how to compute in the context of λ-deformations of current algebras and coset CFTs the exact in the deformation parameters C-function for a wide class of integrable theories that interpolate between a UV and an IR point. We explicitly consider RG flows for integrable deformations of left-right asymmetric current algebras and coset CFTs. In all cases, the derived exact C-functions obey all the properties asserted by Zamolodchikov's c-theorem in two-dimensions.
We investigate the stability of the non-supersymmetric solutions of type-IIB supergravity having an unwarped AdS factor and λ-deformed subspaces found in [26]. Among the plethora of solutions we study the perturbative stability of backgrounds with an AdSn, with n = 3, 4, 6, factor. Our analysis is performed from a lower dimensional effective theory which we construct. We uncover the regions and isolated points in the parameter space of potential perturbative stability.
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