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.

arXiv comment27 pages, 6 figures; v4: minor corrections

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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
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