D-brane Potentials in the Warped Resolved Conifold and Natural Inflation
Zachary Kenton, Steven Thomas
TL;DR
This work addresses embedding Natural Inflation in string theory by exploiting open-string brane moduli in a warped throat geometry. The authors derive exact Laplace-eigenfunction solutions on the Warped Resolved Conifold and show that a wrapped D5-brane with flux can produce a cosine potential for an angular inflaton with a Planckian decay constant, while keeping backreaction under control. They demonstrate that a single D3-brane cannot achieve the required Planckian $f$, but a wrapped D5-brane setup can realize $f\approx 5M_p$ and a GUT-scale inflation potential, with a metastable radial minimum near the tip ensuring slow-roll along the angular direction. The paper also discusses moduli stabilization considerations, backreaction estimates, and future directions for more general brane motions and moduli analysis in the WRC framework.
Abstract
In this paper we obtain a model of Natural Inflation from string theory with a Planckian decay constant. We investigate D-brane dynamics in the background of the warped resolved conifold (WRC) throat approximation of Type IIB string compactifications on Calabi-Yau manifolds. When we glue the throat to a compact bulk Calabi-Yau, we generate a D-brane potential which is a solution to the Laplace equation on the resolved conifold. We can exactly solve this equation, including dependence on the angular coordinates. The solutions are valid down to the tip of the resolved conifold, which is not the case for the more commonly used deformed conifold. This allows us to exploit the effect of the warping, which is strongest at the tip. We inflate near the tip using an angular coordinate of a D5-brane in the WRC which has a discrete shift symmetry, and feels a cosine potential, giving us a model of Natural Inflation, from which it is possible to get a Planckian decay constant whilst maintaining control over the backreaction. This is because the decay constant for a wrapped brane contains powers of the warp factor, and so can be made large, while the wrapping parameter can be kept small enough so that backreaction is under control.