Duality invariant string beta functions at two loops

Abstract

We compute, for cosmological backgrounds, the $O(d,d;\mathbb{R})$ invariant beta functions for the sigma model of the bosonic string at two loops. This yields an independent first-principle derivation of the order ${\alpha }^{\prime }$ corrections to the cosmological target-space equations. To this end we revisit the quantum consistency of Tseytlin's duality invariant formulation of the worldsheet theory. While we confirm the absence of gravitational (and hence Lorentz) anomalies, our results show that the minimal subtraction scheme is not applicable, implying significant technical complications at higher loops. To circumvent these we then change gears and use the Polyakov action for cosmological backgrounds, applying a suitable perturbation scheme that, although not $O(d,d;\mathbb{R})$ invariant, allows one to efficiently determine the $O(d,d;\mathbb{R})$ invariant beta functions.

v2: reference added, version to appear in JHEP

References in corpus (12)

• Double Field Theory
• Double Field Theory at Order ${\alpha }^{\prime }$
• Background Field Equations for the Duality Symmetric String
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• General String Cosmologies at Order ${\alpha }^{\prime }{}^3$
• ${\alpha }^{\prime }$-corrections and their double formulation
• Beta functions for the duality-invariant sigma model
• Dimensional reduction of higher derivative heterotic supergravity
• Consistent gravitational anomalies for chiral bosons
• The Duality Symmetric String at Two-loops

Cited by in corpus (2)

• An ${\alpha }^{\prime }$-complete theory of cosmology and its tensionless limit
• Non-linear stability of ${\alpha }^{\prime }$-corrected Friedmann equations