Update of D3/D7-Brane Inflation on K3 x T^2/Z_2

TL;DR

The paper revisits D3/D7-brane inflation on $K3\times T^{2}/\mathbb{Z}_{2}$, incorporating g_s-corrected gaugino-condensation and flux-induced partial SUSY breaking to ${\cal N}=1$. It validates the holomorphicity of the D7 gauge kinetic function after SUSY breaking and traces the inflaton shift symmetry through quantum corrections, revealing how threshold effects and gaugino condensation alter the inflationary potential. A key result is that the inflaton field range can be parametrically enhanced for highly asymmetric torus complex structure, while the model accommodates both a scenario with an 11% cosmic-string contribution and a WMAP5-compatible case without strings; quantum corrections also permit a regime of eternal inflation. The work links explicit stringy computations (threshold corrections, theta-function embeddings) to cosmological predictions, highlighting tunable aspects of the spectral index and tensor modes within a controllable brane setup. Overall, the study provides a detailed, phenomenologically rich framework to explore brane-inflation with stabilized bulk moduli and string-inspired corrections.

Abstract

We update the D3/D7-brane inflation model on K3 x T^2/Z_2 with branes and fluxes. For this purpose, we study the low energy theory including g_s corrections to the gaugino condensate superpotential that stabilizes the K3 volume modulus. The gauge kinetic function is verified to become holomorphic when the original N=2 supersymmetry is spontaneously broken to N=1 by bulk fluxes. From the underlying classical N=2 supergravity, the theory inherits a shift symmetry which provides the inflaton with a naturally flat potential. We analyze the fate of this shift symmetry after the inclusion of quantum corrections. The field range of the inflaton is found to depend significantly on the complex structure of the torus but is independent of its volume. This allows for a large kinematical field range for the inflaton. Furthermore, we show that the D3/D7 model may lead to a realization of the recent CMB fit by Hindmarsh et al. with an 11% contribution from cosmic strings and a spectral index close to n_s=1. On the other hand, by a slight change of the parameters of the model one can strongly suppress the cosmic string contribution and reduce the spectral index n_s to fit the WMAP5 data in the absence of cosmic strings. We also demonstrate that the inclusion of quantum corrections allows for a regime of eternal D3/D7 inflation.

Figures (8)

• Figure 1: The torus has base length $(2 \pi)^{-1/2}$ (in dimensionless supergravity fields) and $t_2<0$.
• Figure 2: The simplest brane setup on the pillow.
• Figure 3: The function $|\delta|$ with $\delta$ given by \ref{['delta']} for ${\rm Re}(t)=0.26$.
• Figure 4: The function $\tilde{m}^2$ given in \ref{['tildem']} as a function of $-{\rm Im}(t)$ for ${\rm Re}(t)=0.26$ (we chose the values $a = 8\pi^2/10$ and $\Upsilon=2\pi^3/30$, i.e. $c=-10$).
• Figure 5: The inflaton potential $V(\phi)$ including the negative mass term $-\frac{m^2}{2}\phi^2$, which results from stringy corrections. The potential is shown in units of $10^{{-17}}$ for a particular case $g= 10^{-2}$, $\xi = 10^{{-6}}$, for several different values of $m^{2}$. The upper line corresponds to the case $m^{2} = 0$, i.e. to the theory without stringy corrections. For all sufficiently small $m^{2}$, the potential acquires a maximum, which allows the regime of eternal inflation starting from the top of the potential.