Exact results from the geometry of couplings and the effective action

Abstract

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 $\sigma$-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.

arXiv comment1+60 pages, minor improvements, published version

References in corpus (42)

• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Dual Non-Abelian Duality and the Drinfeld Double
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Integrability of the bi-Yang-Baxter sigma-model
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Spacetimes for λ-deformations
• Invariant tensors for simple groups
• The all-loop non-Abelian Thirring model and its RG flow
• Supergravity background of lambda-deformed model for AdS2 x S2 supercoset
• A new family of $SU(2)$ symmetric integrable sigma models
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• On the Beta Function for Anisotropic Current Interactions in 2D
• Integrable flows between exact CFTs
• Duality-invariant class of two-dimensional field theories
• Assembling integrable sigma-models as affine Gaudin models
• $\lambda$-deformations of left-right asymmetric CFTs
• Integrable coupled sigma-models
• All-loop correlators of integrable $\lambda$-deformed $\sigma$-models
• All-loop anomalous dimensions in integrable $\lambda$-deformed $\sigma$-models
• Double and cyclic $\lambda$-deformations and their canonical equivalents
• Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs
• The anisotropic λ-deformed SU(2) model is integrable
• Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
• Chiral stabilization of the renormalization group for flavor and color anisotropic current interactions
• Quantum aspects of doubly deformed CFTs
• RG flows for $\lambda$-deformed CFTs
• Integrable Lambda Models And Chern-Simons Theories
• The exact $C$-function in integrable $\lambda$-deformed theories
• Lambda Models From Chern-Simons Theories
• Weyl anomaly and the $C$-function in $\lambda$-deformed CFTs
• Scalar fields on λ-deformed cosets

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• An exact symmetry in $\lambda$-deformed CFTs
• Krylov complexity of deformed conformal field theories
• Field theory and $\lambda$-deformations: Expanding around the identity
• Hamiltonian integrability of the webs of integrable theories
• Webs of integrable theories
• A free field perspective of $\lambda$-deformed coset CFT's
• Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production
• Classical solutions of $\lambda$-deformed coset models
• $\lambda$-deformations in the upper-half plane
• A generalized method for all-loop results in $\lambda$-models