Chasing Brane Inflation in String-Theory

TL;DR

The paper analyzes embedding brane–antibrane inflation in a fully moduli-fixed type IIB setup, focusing on a D3-brane inflaton in a warped conifold with D7 embeddings and a terminal anti-D3 at the tip. By deriving the F-term potential with a general D7 embedding and stabilizing all closed-string moduli, it constructs the effective single-field potential V(φ) and probes two explicit embeddings, Ouyang and Kuperstein. It finds that global cancellations of moduli-stabilization forces are not generically possible; only the Kuperstein case can, with fine-tuning, produce a flat inflection point, while the Coulomb term remains subleading in most regions. The results suggest significant challenges to realizing slow-roll brane inflation in these fixed-moduli string compactifications and point toward exploring alternative inflationary mechanisms within or beyond this framework.

Abstract

We investigate the embedding of brane anti-brane inflation into a concrete type IIB string theory compactification with all moduli fixed. Specifically, we are considering a D3-brane, whose position represents the inflaton $φ$, in a warped conifold throat in the presence of supersymmetrically embedded D7-branes and an anti D3-brane localized at the tip of the warped conifold cone. After presenting the moduli stabilization analysis for a general D7-brane embedding, we concentrate on two explicit models, the Ouyang and the Kuperstein embeddings. We analyze whether the forces, induced by moduli stabilization and acting on the D3-brane, might cancel by fine-tuning such as to leave us with the original Coulomb attraction of the anti D3-brane as the driving force for inflation. For a large class of D7-brane embeddings we obtain a negative result. Cancelations are possible only for very small intervals of $φ$ around an inflection point but not globally. For the most part of its motion the inflaton then feels a steep, non slow-roll potential. We study the inflationary dynamics induced by this potential.

Figures (5)

• Figure 1: The plots display the inflaton potential $V(\phi)$ for the Kuperstein embedding for two different values of the uplifting parameter $\beta=1.21$ (left) $\beta=1.4$ (right). The left plots shows that finetuning allows to get rid of the potential hill, leaving only an inflection point suitable for inflation. The right plot shows the non-finetuned generic situation: the potential has two separate critical points and an inflection point in between, thus creating a potential barrier. To move down the throat (towards smaller $\phi$) the inflaton has to cross the barrier and run uphill over a certain interval.
• Figure 2: On the left: the dependence of the potential on $\phi$ and $\sigma$ near the minimum. The black thick line is the value of $\sigma_{c}$ one would get neglecting the uplifting term (using just eq. (\ref{['sigma0']})). Clearly if one is interested in inflation dynamics, neglecting $V_{\rm up}$ is inconsistent. On the right: the black thin lines are the potential (times $10^{16}$) evaluated for different but $\phi$ independent $\sigma_{c}$. The red thick line is obtained plotting $V(\phi,\sigma_{c}(\phi))$ (times $10^{16}$). Again one clearly sees that it is inconsistent to study inflation just in the $\phi$ direction for fixed $\sigma_{c}$
• Figure 3: The plot shows the potential $V(\phi)$ (red) and the slow-roll parameters $\eta(\phi)$ (blue) and $\epsilon(\phi)$ (black). The latter is so small that it can hardly be distinguished from the $\phi$ axis. Next to the tip of the throat the potential has generically a maximum and a minimum. For $\phi$ large enough the potential grows like $\phi^2$ and $\eta$ is of order one (or bigger). But for $\phi\rightarrow 0$ the curvature of the potential changes at the inflection point and $\eta$ switches sign (and eventually diverges at $\phi=0$).
• Figure 4: The figure summarizes our overshoot analysis. The continuous line is the actual potential, the darker dashed line refers to the discussion of the damped oscillatory phase and the lighter dashed line refers to the uphill phase.
• Figure 5: The plot shows the discriminant, eq. (\ref{['discri']}), as a function of $\beta$ (without performing the $\Delta/\sigma_0$ expansion). When the discriminant is zero the minimum and maximum of the potential coincide and we get a flat inflection point.