Dimensional reduction for D3-brane moduli

Abstract

Warped string compactifications are central to many attempts to stabilize moduli and connect string theory with cosmology and particle phenomenology. We present a first-principles derivation of the low-energy 4D effective theory from dimensional reduction of a D3-brane in a warped Calabi-Yau compactification of type IIB string theory with imaginary self-dual 3-form flux, including effects of D3-brane motion beyond the probe approximation, and find the metric on the moduli space of brane positions, the universal volume modulus, and axions descending from the 4-form potential. As D3-branes may be considered as carrying either electric or magnetic charges for the self-dual 5-form field strength, we present calculations in both duality frames. Our results are consistent with, but extend significantly, earlier results on the low-energy effective theory arising from D3-branes in string compactifications.

The cosmological constant and the electroweak scale

“…While the brane positions are good Kähler moduli for the effective field theory, the presence of D3-branes leads a redefinition of both the Kähler coordinate T and the term K K in the Kähler potential (2.1). Using Φ i = Z i /2πα and setting momentarily ξ = 0, we have [22][23][24]…”

Variations on the Dirac string

“…Then, as we suggested in the section above, take N at any fixed time to be the line segment from X * to X. Then we can 4 This is the approach taken in [13] for D3-branes. choose a static gauge 5 t = Y 0 (τ, σ) = τ and Y (τ, σ) = X * + σδ X(t) with 0 ≤ σ ≤ 1.…”

“…It is particularly helpful for a careful accounting of degrees of freedom, as needed in dimensional reduction. Determining the lower-dimensional effective action is also an off-shell calculation, and extra terms from the generalized Dirac string worldvolume (which vanish on-shell) are critical to account for all the kinetic terms required by supergravity [10,13]. ACKNOWLEDGMENTS AF would like to thank K. Dasgupta, N. Afshordi, and L. Boyle for interesting discussions.…”

Warped Kähler potentials and fluxes

“…The only difference is that the matrix M ab (denoted by M ab w in [1]) now contains also the manifestly G 3 dependent term appearing in (2.37). Furthermore, by looking at the kinetic terms for Imρ a in (2.41), we recognise the terms obtained in [22,25] by freezing the non-universal Kähler moduli and focusing on the C 4 -moduli, including such explicitly G 3 dependent contribution. Hence our effective theory provides the manifestly supersymmetric completion of the results of [22,25], consistently combining the different possible moduli of this class of flux compactifications.…”

“…Namely, the authors of [22] performed a direct and careful dimensional reduction which focuses on the C 4 -moduli and keeps the (non-universal) Kähler moduli fixed -see also the very recent [25] for a similar derivation including mobile D3-branes. Hence, the results of the present paper provide a manifestly supersymmetric completion of the results of [22,25] and resolve the apparent conflict between the approaches adopted in [22,25] and in [5,6,1].…”