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arXiv · 2209.05502

Universal 1-loop divergences for integrable sigma models

Nat Levine
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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.

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Nat Levine. 2022-09-12. Universal 1-loop divergences for integrable sigma models. https://doi.org/10.1007/jhep03(2023)003

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