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.

23 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

References in corpus (7)

• Double Field Theory
• Double Field Theory at Order ${\alpha }^{\prime }$
• Frame-like Geometry of Double Field Theory
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• General String Cosmologies at Order ${\alpha }^{\prime }{}^3$
• String theory at order ${\alpha }^{\prime 2}$ and the generalized Bergshoeff-de Roo identification

Cited by in corpus (2)

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