String Theory and Hybrid Inflation/Acceleration

TL;DR

The paper constructs a concrete string-theoretic realization of hybrid P-term inflation by mapping an $\,\mathcal{N}=2$ gauge theory with Fayet–Iliopoulos terms to a Hanany–Witten brane configuration (NS5–D4–D6). Inflation arises on the Coulomb branch due to a one-loop lifting of a flat direction, while a tachyonic instability triggers a waterfall to a fully Higgsed, SUSY ground state, with the open-string one-loop potential matching field-theory results. A detailed string theory–cosmology dictionary relates brane parameters ($g_{YM}$, $\xi$, $|\Phi_3|$, $\Delta L$) to cosmological observables, enabling constraints from COBE and dark-energy data on the brane setup. The work also reveals a level-by-level vanishing supertrace (a stringy Zeeman effect) and connects tachyon condensation in this context to tachyonic preheating scenarios, offering insights into SUSY breaking patterns and the late-time acceleration within a stringy framework.

Abstract

We find a description of hybrid inflation in (3+1)-dimensions using brane dynamics of Hanany-Witten type. P-term inflation/acceleration of the universe with the hybrid potential has a slow-roll de Sitter stage and a waterfall stage which leads towards an N=2 supersymmetric ground state. We identify the slow-roll stage of inflation with a non-supersymmetric `Coulomb phase' with Fayet-Iliopoulos term. This stage ends when the mass squared of one of the scalars in the hypermultiplet becomes negative. At that moment the brane system starts undergoing a phase transition via tachyon condensation to a fully Higgsed supersymmetric vacuum which is the absolute ground state of P-term inflation. A string theory/cosmology dictionary is provided, which leads to constraints on parameters of the brane construction from cosmological experiments. We display a splitting of mass levels reminiscent of the Zeeman effect due to spontaneous supersymmetry breaking.

Figures (5)

• Figure 1: Cosmological potential with Fayet-Iliopoulos term. De Sitter valley is classically flat; it is lifted by the one-loop correction corresponding to the one-loop potential between $D4$-$D6$. In this figure the valley is along the $|\Phi_3|$ axis; the orthogonal direction is a line passing through the origin of the complex $\Phi_2$ plane and we have put $|\Phi_1|=0$. Notice there is no $\mathbb{Z}_2$ symmetry of the ground state, it is just a cross section of the full $U(1)$ symmetry corresponding to the phase of the complex $\Phi_2$ field. The fields are shown in units of $\sqrt{\xi/ g}$. The bifurcation point corresponds to $|\Phi_3| = \sqrt{\xi/g}$, $\Phi_2 = 0$. The absolute minimum is at $\Phi_3 = 0$, $\Phi_2= \sqrt{2\xi/ g}$.
• Figure 2: Cosmological potential without Fayet-Iliopoulos term. The motion of the D4 corresponds to moving along the bottom of the valley, which has a zero potential.
• Figure 3: Brane configuration without Fayet-Iliopoulos term. We are free to move D4 in 4,5 directions with no energy cost.
• Figure 4: Brane configuration evolution with Fayet-Iliopoulos term. a) For $\phi\neq 0$, supersymmetry is broken and D4-D6 experience an attractive force. b) At the bifurcation point, a complex scalar in the hypermultiplet becomes massless; when we overshoot tachyon instability forms, taking the system to a zero energy ground state shown in c) .
• Figure 5: Splitting of mass for the first three levels due to the presence of an angle $\phi$. Notice that at each level the supertrace vanishes. On the right we show the number of bosonic (B) or fermionic (F) states with such mass for either the 4-6 or 6-4 strings. The total number of states is twice as many.