Abstract
In string theory compactifications it is common to find an effective Lagrangian for the scalar fields with a non-canonical kinetic term. We study the effective action of the scalar position moduli of Type II Dp-branes. In many instances the kinetic terms are in fact modified by a term proportional to the scalar potential itself. This can be linked to the appearance of higher-dimensional supersymmetric operators correcting the Kahler potential. We identify the supersymmetric dimension-eight operators describing the α′ corrections captured by the D-brane Dirac-Born-Infeld action. Our analysis then allows an embedding of the D-brane moduli effective action into an $$ \mathcal{N}=1 $$ supergravity formulation. The effects of the potential-dependent kinetic terms may be very important if one of the scalars is the inflaton, since they lead to a flattening of the scalar potential. We analyze this flattening effect in detail and compute its impact on the CMB observables for single-field inflation with monomial potentials.
Highlights
A classification of such operators was presented in [4]
We study the effective action of the scalar position moduli of Type II Dp-branes
A particular ghost-free linear combination of them has been singled out, it reads dθ2dθ2DαΦDαΦDα Φ Dα Φ. This operator and its component expression are simple and “clean” for a number of reasons, and it has the potential advantage that it can be coupled to N = 1 supergravity in a straight-forward manner [9]. As discussed below, it is not the operator we find in the effective action of D-branes in Type II string theory
Summary
The four-dimensional effective theory for the bosonic open string fields of Dp-branes can be derived from the DBI and CS actions describing the world-volume deformations of the brane. The DBI action is exact in α up to second derivatives of the scalars, leading to a clear advantage over the standard supergravity description of the effective theory for open string moduli in which α corrections are in general not known or highly difficult to compute.1 We find that these α corrections affect the kinetic term, giving rise to a non-canonical normalization as advanced in the Introduction. In the absence of mixed Minkowski-internal tensors, i.e., gμa = Bμa = 0, and considering a constant internal profile for the position moduli, ∂aφ = 0, the world-volume determinant can be factorized as det(P [EMN + σFMN ]) = det gs1/2Z−1/2ημν + gs1/2Z1/2σ2∂μφm∂ν φn det gs1/2gab + σFab − Bab .
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