O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality

Abstract

We show that the one- and two-loop $\beta$-functions of the closed, bosonic string can be written in a manifestly O($D$,$D$)-covariant form. Based on this result, we prove that 1) Poisson-Lie symmetric $\sigma$-models are two-loop renormalisable and 2) their $\beta$-functions are invariant under Poisson-Lie T-duality. Moreover, we identify a distinguished scheme in which Poisson-Lie symmetry is manifest. It simplifies the calculation of two-loop $\beta$-functions significantly and thereby provides a powerful new tool to advance into the quantum regime of integrable $\sigma$-models and generalised T-dualities. As an illustrating example, we present the two-loop $\beta$-functions of the integrable $\lambda$- and $\eta$-deformation.

44 pages, 2 tables

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Cited by in corpus (10)

• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• Consistent Truncations and Dualities
• The Magic Renormalisability of Affine Gaudin Models
• The Heterotic-Ricci flow and its three-dimensional solitons
• Type IIA embeddings of $D=5$ minimal gauged supergravity via Non-Abelian T-duality
• Hamiltonian integrability of the webs of integrable theories
• On a class of conformal $\mathcal{E}$-models and their chiral Poisson algebras
• Poisson-Lie T-duality defects and target space fusion
• Duality invariant string beta functions at two loops
• Duality covariant field redefinitions