Minimal independent couplings at order ${\alpha }^{\prime 2}$

Abstract

Using field redefinitions and Bianchi identities on the general form of the effective action for metric, $B$-field and dilaton, we have found that the minimum number of independent couplings at order ${\alpha }^{\prime 2}$ is 60. We write these couplings in two different schemes in the string frame. In the first scheme, each coupling does not include terms with more than two derivatives and it does not include structures $R,R_{\mu \nu },{\nabla }_{\mu }{H}^{\mu \alpha \beta }$, ${\nabla }_{\mu }{\nabla }^{\mu }\Phi$. In this scheme, 20 couplings which are the minimum number of couplings for metric and $B$-field, include dilaton trivially as the overall factor of $e^{-2\Phi }$, and all other couplings include derivatives of dilaton. In the second scheme, the dilaton appears in all 60 coupling only as the overall factor of $e^{-2\Phi }$. In this scheme, 20 of the couplings are exactly the same as those in the previous scheme.

arXiv comment17 pages, Latex file, no figure

References in corpus (15)

• String Theory Dynamics In Various Dimensions
• Double Field Theory
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Effects of D-instantons
• Background independent action for double field theory
• xTras: a field-theory inspired xAct package for Mathematica
• T-duality and ${\alpha }^{\prime }$-corrections
• The Odd story of ${\alpha }^{\prime }$-corrections
• Duality constraints on effective actions
• Four-derivative couplings via T-duality constraint
• Second order higher-derivative corrections in Double Field Theory
• Modular Forms and $SL(2,\mathbb{Z})$-covariance of type IIB superstring theory
• $R^4$ terms in supergravities via T-duality constraint
• Type I/heterotic duality and M-theory amplitudes
• T-duality invariant effective actions at orders ${\alpha }^{\prime },{\alpha }^{\prime 2}$

Cited by in corpus (12)

• Duality Invariance and Higher Derivatives
• On NS-NS couplings at order ${\alpha }^{\prime 3}$
• Minimal gauge invariant couplings at order ${\alpha }^{\prime 3}$: NS-NS fields
• Background independence of effective actions at critical dimension
• Effective action of string theory at order ${\alpha }^{\prime }$ in the presence of boundary
• 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 ${\alpha }^{\prime 2}$
• Higher-derivative couplings and torsional Riemann curvature
• Surface terms in effective action of O-plane at order ${\alpha }^{\prime 2}$
• Six-Derivative Yang-Mills Couplings in Heterotic String Theory
• T-duality of D-brane versus O-plane actions
• Minimal gauge invariant couplings at order ${\ell }_p^6$ in M-theory