Abstract
We show that the one- and two-loop β-functions of the closed, bosonic string can be written in a manifestly O(D,D)-covariant form. Based on this result, we prove that1) Poisson-Lie symmetric σ-models are two-loop renormalisable and2) their β-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 β-functions significantly and thereby provides a powerful new tool to advance into the quantum regime of integrable σ-models and generalised T-dualities. As an illustrating example, we present the two-loop β-functions of the integrable λ- and η-deformation.
Highlights
Two seemingly completely different theories, for example, one strongly coupled and the other one weakly coupled, may still exhibit the same physics
The generalised fluxes and their derivatives transform anomalous under this rotation, the particular combination in which they enter the β-function cancels all anomalous contributions. This is a standard result in the flux formulation of double field theory (DFT) [54, 58], but since double Lorentz rotations become much more subtle beyond one-loop, we want to review how it arises: the finite transformation ΛAB is a composition of infinitesimal transformations, namely ΛAB = exp(λAB) with λAB = −λBA
3) The respective RG flows are invariant under PL T-duality
Summary
Two seemingly completely different theories, for example, one strongly coupled and the other one weakly coupled, may still exhibit the same physics. 2) A second problem is that the resulting, dual target space geometry has in general a smaller isometry group which seemingly prohibits the duality to be inverted. Insights from double field theory (DFT) [37, 39] were used to show that PL T-duality with adapted transformation rules maps CFTs to CFTs [42] Motivated by these findings we will use DFT techniques to compute β-functions for PL σ-models and show that they are renormalisable.
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