On D3-brane potentials in compactifications with fluxes and wrapped D-branes

Abstract

We study the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes. If the Kähler moduli of the compact space are stabilized by nonperturbative effects, a D3-brane experiences a force due to its interaction with D-branes wrapping certain four-cycles. We compute this interaction, as a correction to the warped four-cycle volume, using explicit throat backgrounds in supergravity. This amounts to a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume. We demonstrate for warped conical spaces that the superpotential correction is given by the embedding equation specifying the wrapped four-cycle, in agreement with the general form proposed by Ganor. Our approach automatically provides a solution to the problem of defining a holomorphic gauge coupling on wrapped D7-branes in a background with D3-branes. Finally, our results have applications to cosmological inflation models in which the inflaton is modeled by a D3-brane moving in a warped throat. February 1, 2008 1. Euclidean D3-branes wrapping a four-cycle in the Calabi-Yau [22].

Inflation and String Theory

“…These conditions can be expressed most simply in terms of an auxiliary eight-dimensional geometry Y , in which the axiodilaton τ parameterizes an elliptic fibration over the six-dimensional manifold X on which the type IIB theory is compactified. 20 This construction is known as 19 Supersymmetry requires that the superpotential is a holomorphic function of the moduli, but verifying that V 4 is the real part of a holomorphic function is highly non-trivial [218,335]. When D3-branes are present, their backreaction on the volume V 4 must be incorporated in order to maintain holomorphy [335].…”

Large nonlocal non-Gaussianity from a curvaton brane

“…For example, since the compact Calabi-Yau manifold cannot have exact continuous isometries, the isometries of the bulk must be broken when the finite throat is glued on this bulk, and then the warp factor dependents on angles. Moreover, a nonperturbative effect which stabilizes the Kähler moduli could bring a potential for the branes [30][31][32]. The form of this potential depends on the precise embedding of the wrapped branes.…”

Gauge-String Dualities and some Applications

“…where δh(0, r) is the perturbation of the warped factor at the position of the D3-brane r = 0, caused by the D3-brane at radial coordinate r. For a D3-brane far from the tip of the throat, with radial coordinate r ≫ ε 2/3 , δh(0, r) ≈ 27/(32π 2 T3r 4 ) [119]. Thus, the potential assumes the form [116,120] (note that the definition of r 2 here differs by a factor of 3/2 from that in [119])…”

“…Thus, the potential assumes the form [116,120] (note that the definition of r 2 here differs by a factor of 3/2 from that in [119])…”

“…This correction depends on the D3-brane position and is responsible for the prefactor A(zα) [128]. In [119], D3-brane backreaction on the warped four-cycle volume was calculated leading to a simple formula…”