$R^4$ terms in supergravities via T-duality constraint

Abstract

It has been speculated in the literature that the effective actions of string theories at any order of ${\alpha }^{\prime }$ should be invariant under the Buscher rules plus their higher covariant derivative corrections. This may be used as a constraint to find effective actions at any order of ${\alpha }^{\prime }$, in particular, the metric, the B-field and the dilaton couplings in supergravities at order ${\alpha }^{\prime 3}$ up to an overall factor. For the simple case of zero B-field and diagonal metric in which we have done the calculations explicitly, we have found that the constraint fixes almost all the seven independent Riemann curvature couplings. There is only one term which is not fixed, because when metric is diagonal, the reduction of two $R^4$ terms become identical. The Riemann curvature couplings that the T-duality constraint produces for both type II and Heterotic theories are fully consistent with the existing couplings in the literature which have been found by the S-matrix and by the sigma-model approaches.

arXiv comment20 pages, Latex file, no figure;V2: minor modifications, it appears in PRD

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Cited by in corpus (20)

• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• Effective action of bosonic string theory at order ${\alpha }^{\prime 2}$
• Four-derivative couplings via T-duality constraint
• String Dualities at Order ${\alpha }^{\prime 3}$
• Generalized Dualities and Higher Derivatives
• Minimal independent couplings at order ${\alpha }^{\prime 2}$
• Duality-invariant extensions of Einstein-Maxwell theory
• The generalized Bergshoeff-de Roo identification II
• Minimal gauge invariant couplings at order ${\alpha }^{\prime 3}$: NS-NS fields
• Supersymmetry, T-duality and Heterotic ${\alpha }^{\prime }$-corrections
• Background independence of effective actions at critical dimension
• Higher-derivative field redefinitions in the presence of boundary
• Effective action of string theory at order ${\alpha }^{\prime }$ in the presence of boundary
• ${\alpha }^{\prime }$-corrections to DBI action via T-duality constraint
• O-plane couplings at order ${\alpha }^{\prime 2}$: one R-R field strength
• Couplings of order six in the gauge field strength and the second fundamental form on a D${}_p$-brane at order ${\alpha }^{\prime 2}$
• T-duality constraint on R-R couplings
• $O(D,D)$-constraint on $D$-dimensional effective actions
• Six-Derivative Yang-Mills Couplings in Heterotic String Theory
• T-duality of D-brane versus O-plane actions