Green-Schwarz Mechanism for String Dualities

Abstract

We determine the complete spacetime action to first order in ${\alpha }^{\prime }$ for the massless fields of bosonic string theory compactified on a $d$-dimensional torus. A fully systematic procedure is developed that brings the action into a minimal form in which all fields apart from the metric enter only with first-order derivatives. T-duality implies that this action must have a global $\mathrm{O}(d,d,\mathbb{R})$ symmetry, and we show that this requires a Green-Schwarz type mechanism for ${\alpha }^{\prime }$-deformed $\mathrm{O}(d,d,\mathbb{R})$ transformations. In terms of a frame formalism with $\mathrm{GL}(d)\times \mathrm{GL}(d)$ gauge symmetry this amounts to a modification of the three-form curvature by a Chern-Simons term for composite gauge fields.

arXiv comment9 pages, v2: some corrected typos and corrected Eq. (12). Published version

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Cited by in corpus (16)

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• Quantum correction to generalized T-dualities
• Duality Invariance and Higher Derivatives
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• String Dualities at Order ${\alpha }^{\prime 3}$
• O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'
• General String Cosmologies at Order ${\alpha }^{\prime }{}^3$
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• The generalized Bergshoeff-de Roo identification II
• The $\beta$-symmetry of supergravity
• ${\alpha }^{\prime }$-corrections and their double formulation
• Derive Lovelock Gravity from String Theory in Cosmological Background
• Old Dualities and New Anomalies
• Beta functions for the duality-invariant sigma model
• Duality invariant string beta functions at two loops
• Revisiting Schwarzschild black hole singularity through string theory