Completing $R^4$ using $O(d,d)$

Abstract

The tree-level string effective action is known to contain quartic Riemann terms with coefficient $\zeta (3){\alpha }^{\prime 3}$. In the case of the type II string this is the first ${\alpha }^{\prime }$ correction. We use the requirement that the action reduced on a $d$-torus should have an $O(d,d)$ symmetry to find the B-field couplings up to fifth order in fields. The answer turns out to have a surprisingly intricate structure.

arXiv comment23 pages; v2: Clarifications and details of comparison to literature added; v3: Added argument that condition imposed is also sufficient for O(d,d). Published version

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Cited by in corpus (2)

• T-duality building blocks for ${\alpha }^{\prime }$ string corrections
• Higher-derivative couplings and torsional Riemann curvature