S-duality invariant dilaton couplings at order ${\alpha }^{\prime 3}$

Abstract

The Riemann curvature correction to the type II supergravity at eight-derivative level is given schematically as $(t_8t_8+{1}{8}\eps_{10}\eps_{10})R^4$ at tree-level. The replacement of the generalized Riemann curvature in $t_8{t}_8{R}^4$, proposed by Gross and Sloan, produces various NS-NS couplings which are invariant under T-duality. Recently, using the combination of S-duality and T-duality transformations on these couplings, we have found groups of couplings which are invariant under the S-duality transformation. In this paper, we have examined the couplings involving the dilaton with direct scattering amplitude calculations of four NS-NS vertex operators in the superstring theory and found exact agreement. The coupling $\eps_{10}\eps_{10}R^4$ is a total derivative term at four-field level. The $\sigma$-model beta function approach implies the presence of this term at the tree-level. By examining the sphere-level scattering amplitude of five gravitons, we have also confirmed the presence of this term in the tree-level effective action.

15 pages, Latex file, no figure; v4: the version appears in JHEP

References in corpus (4)

• The One-Loop Five-Graviton Amplitude and the Effective Action
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Higher genus superstring amplitudes from the geometry of moduli spaces
• The D^6 R^4 term in type IIB string theory on T^2 and U-duality

Cited by in corpus (7)

• Duality constraints on effective actions
• String Dualities at Order ${\alpha }^{\prime 3}$
• $R^4$ terms in supergravities via T-duality constraint
• Sphere-level Ramond-Ramond couplings in Ramond-Neveu-Schwarz formalism
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• Higher-derivative couplings and torsional Riemann curvature
• S-duality constraint on higher-derivative couplings