T-duality invariant effective actions at orders ${\alpha }^{\prime },{\alpha }^{\prime 2}$

Abstract

We use compatibility of the $D$-dimensional effective actions for diagonal metric and for dilaton with the T-duality when theory is compactified on a circle, to find the the $D$-dimensional couplings of curvatures and dilaton as well as the higher derivative corrections to the $(D-1)$-dimensional Buscher rules at orders ${\alpha }^{\prime }$ and ${\alpha }^{\prime 2}$. We observe that the T-duality constraint on the effective actions fixes the covariant effective actions at each order of ${\alpha }^{\prime }$ up to field redefinitions and up to an overall factor. Inspired by these results, we speculate that the $D$-dimensional effective actions at any order of ${\alpha }^{\prime }$ must be consistent with the standard Buscher rules provided that one uses covariant field redefinitions in the corresponding reduced $(D-1)$-dimensional effective actions. This constraint may be used to find effective actions at all higher orders of ${\alpha }^{\prime }$.

arXiv comment24 pages, latex file, no figure; v2: major modifications; v3: the version appears in JHEP

References in corpus (10)

• Double Field Theory
• Background independent action for double field theory
• Symmetries of higher-order string gravity actions
• T-duality and ${\alpha }^{\prime }$-corrections
• The Odd story of ${\alpha }^{\prime }$-corrections
• Duality constraints on effective actions
• Duality completion of higher derivative corrections
• Higher Derivative Corrections to O-plane Actions: NS-NS Sector
• T-duality of D-brane action at order ${\alpha }^{\prime }$ in bosonic string theory
• T-duality of ${\alpha }^{\prime }$-correction to DBI action at all orders of gauge field

Cited by in corpus (7)

• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• Four-derivative couplings via T-duality constraint
• $R^4$ terms in supergravities via T-duality constraint
• Minimal independent couplings at order ${\alpha }^{\prime 2}$
• Minimal gauge invariant couplings at order ${\alpha }^{\prime 3}$: NS-NS fields
• The generalized Bergshoeff-de Roo identification II
• $O(D,D)$-constraint on $D$-dimensional effective actions