D3/D7 Inflationary Model and M-theory

TL;DR

The paper presents a D3/D7 inflationary scenario in Type IIB string theory with a constant worldvolume flux on the D7, realized as an $N=2$ $P$-term inflation potential. Inflation proceeds along a Coulomb-like de Sitter valley with the inflaton given by the D3–D7 separation, and ends in a waterfall to a Minkowski vacuum described by a D3/D7 bound state identified with a non-linear (non-commutative) Abelian instanton; the nonzero cosmological constant is tied to resolving the small-instanton singularity via the noncommutative parameter. The construction is embedded in a compactified Type IIB setup on $K3 imes T^2/ ext{Z}_2$ with orientifolds, and lifted to M-theory on a four-fold with G-fluxes, analyzing both Coulomb and Higgs branches, their SUSY properties, and higher-order corrections. The work connects cosmological dynamics to brane/flux configurations, noncommutative instanton physics, and anomaly-consistent M-theory compactifications, offering a path toward a fully string/M-theory realization of hybrid inflation with a geometric origin for the cosmological constant.

Abstract

A proposal is made for a cosmological D3/D7 model with a constant magnetic flux along the D7 world-volume. It describes an N=2 gauge model with Fayet-Iliopoulos terms and the potential of the hybrid P-term inflation. The motion of the D3-brane towards D7 in a phase with spontaneously broken supersymmetry provides a period of slow-roll inflation in the de Sitter valley, the role of the inflaton being played by the distance between D3 and D7-branes. After tachyon condensation a supersymmetric ground state is formed: a D3/D7 bound state corresponding to an Abelian non-linear (non-commutative) instanton. In this model the existence of a non-vanishing cosmological constant is associated with the resolution of the instanton singularity. We discuss a possible embedding of this model into a compactified M-theory setup.

Figures (4)

• Figure 1: The D3/D7 "cosmological" system. The 3-3 strings give rise to the ${\mathcal{N}}=2$ vector multiplet, the 7-3 strings to the hypermultiplet and the worldvolume gauge field ${\mathcal{F}}$ to the FI terms of the $D=4$ gauge theory.
• Figure 2: The "snowman" fibration of the $K3\times K3$ four-fold. The crosses indicate points on the ${\mathbb C}P^1$ basis at which the fibre tori degenerate. In the orbifold limit of the 'top' K3 there will be four such points.
• Figure 3: The initial brane configuration on the "pillow" $T^2/{\mathbb Z}_2$.
• Figure 4: The Coulomb branch. As the system is driven away from the unstable point of figure 2, $T^2/{\mathbb Z}_2 \ \rightarrow {\mathbb C}P^1$, the orientifold planes split into $(p,q)$ 7-branes, and the D3-brane will eventually fall into one D7-brane as an instanton.