Universal 1-loop divergences for integrable sigma models

Abstract

We present a simple, new method for the 1-loop renormalization of integrable $\sigma$-models. By treating equations of motion and Bianchi identities on an equal footing, we derive 'universal' formulae for the 1-loop on-shell divergences, generalizing case-by-case computations in the literature. Given a choice of poles for the classical Lax connection, the divergences take a theory-independent form in terms of the Lax currents (the residues of the poles), assuming a 'completeness' condition on the zero-curvature equations. We compute these divergences for a large class of theories with simple poles in the Lax connection. We also show that $Z_T$ coset models of 'pure-spinor' type and their recently constructed $\eta$- and $\lambda$-deformations are 1-loop renormalizable, and 1-loop scale-invariant when the Killing form vanishes.

27 pages, 6 figures; v4: minor corrections

References in corpus (13)

• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Integrable Deformations of Strings on Symmetric Spaces
• The all-loop non-Abelian Thirring model and its RG flow
• Non-local charges, Zm gradings and coset space actions
• Integrable Deformations of Sigma Models
• Assembling integrable sigma-models as affine Gaudin models
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Unimodular jordanian deformations of integrable superstrings
• Integrable sigma models and 2-loop RG flow
• RG flows of integrable $\sigma$-models and the twist function
• RG flow of integrable $\mathcal{E}$-models
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations

Cited by in corpus (5)

• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• An elliptic integrable deformation of the Principal Chiral Model
• The Magic Renormalisability of Affine Gaudin Models
• Integrability of the $\lambda$-deformation of the PCM with spectators