$\lambda$-deformations in the upper-half plane

Abstract

We formulate $\lambda$-deformed $\sigma$-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter $\lambda$ and for large values of the level $k$ of the underlying WZW model. To perform our computations we use either conformal perturbation theory in association with Cardy's doubling trick, as well as meromorphicity arguments and a non-perturbative symmetry in the parameter space $(\lambda ,k)$, or standard QFT techniques based on the free field expansion of the $\sigma$-model action, with the free fields obeying appropriate boundary conditions. Both methods have their own advantages yielding consistent and rich, compared to those in the absence of a boundary, complementary results. We pay particular attention, albeit not exclusively, to integrability preserving boundary conditions.

arXiv commentv1: 45 pages + 24 pages appendices, v2: NPB version

References in corpus (35)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• D-brane dynamics
• On integrability of the Yang-Baxter $\si$-model
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Conformal Field Theories Near a Boundary in General Dimensions
• D-branes in the WZW model
• Flux Stabilization of D-branes
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• An Integrable Deformation of the AdS5 x S5 Superstring
• 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
• D-branes in group manifolds
• The geometry of WZW branes
• The all-loop non-Abelian Thirring model and its RG flow
• A new family of $SU(2)$ symmetric integrable sigma models
• Lectures on Branes in Curved Backgrounds
• 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
• More D-branes in the Nappi-Witten background
• $\lambda$-deformations of left-right asymmetric CFTs
• All-loop correlators of integrable $\lambda$-deformed $\sigma$-models
• All-loop anomalous dimensions in integrable $\lambda$-deformed $\sigma$-models
• Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs
• Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
• Orientifolds of the 3-sphere
• Brane backreactions and the Fischler-Susskind mechanism in conformal field theory
• Exact results from the geometry of couplings and the effective action
• Field theory and $\lambda$-deformations: Expanding around the identity

Cited by in corpus (3)

• Deformed WZW Models and Hodge Theory -- Part I
• Hamiltonian integrability of the webs of integrable theories
• Integrable branes in generalized $\lambda$-deformations