Holographic Systematics of D-brane Inflation

TL;DR

The paper develops a holographic framework to compute corrections to the D3-brane inflaton potential in warped throat geometries by mapping UV bulk deformations to perturbations of the dual Coulomb branch. It identifies the leading contributions from lowest-dimension operators, Δ=3/2 (chiral) and Δ=2 (non-chiral), whose presence or absence is controlled by discrete bulk symmetries; in the KS throat, the Δ=3/2 term yields a φ^{3/2} potential, while symmetry can force a Δ=2 quadratic term, enabling inflation by balancing against H^2 φ^2. The approach is general and extends to other warped geometries once the KK spectrum is known, offering a unified, symmetry-aware classification of D-brane inflation models and clarifying connections to D7-brane embeddings and current multiplets. This framework provides practical guidance for constructing inflationary scenarios in string theory and addressing the eta problem through controlled UV perturbations.

Abstract

We provide a systematic treatment of possible corrections to the inflaton potential for D-brane inflation in the warped deformed conifold. We consider the D3-brane potential in the presence of the most general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. This corresponds to the potential on the Coulomb branch of the dual gauge theory, in the presence of arbitrary perturbations of the Lagrangian. The leading contributions arise from perturbations by the most relevant operators that do not destroy the throat geometry. We find a generic contribution from a non-chiral operator of dimension $Δ=2$ associated with a global symmetry current, resulting in a negative contribution to the inflaton mass-squared. If the Calabi-Yau preserves certain discrete symmetries, this is the dominant correction to the inflaton potential, and fine-tuning of the inflaton mass is possible. In the absence of such discrete symmetries, the dominant contribution comes from a chiral operator with $Δ=3/2$, corresponding to a $φ^{3/2}$ term in the inflaton potential. The resulting inflationary models are phenomenologically similar to the inflection point scenarios arising from specific D7-brane embeddings, but occur under far more general circumstances. Our strategy extends immediately to other warped geometries, given sufficient knowledge of the Kaluza-Klein spectrum.