On supersymmetric Minkowski vacua in IIB orientifolds

TL;DR

The paper analyzes conditions for supersymmetric Minkowski vacua in type IIB orientifold compactifications with fluxes and racetrack non-perturbative superpotentials. It shows that orbifold models with one or two complex structure moduli and supersymmetric 2-form flux can achieve fully stabilized Minkowski minima, and that including gaugino condensation on fixed D3-branes extends this to models without complex structure moduli. The approach hinges on solving $D_I W=0$ together with $W=0$ for all moduli, using a racetrack superpotential $W_{ ext{np}}$ added to a flux-induced $W_{ ext{flux}}$, and demonstrates positive-definite mass matrices and robustness to perturbative K"ahler corrections at the Minkowski point. The work also details explicit constructions for toroidal orientifolds with one or two complex structure moduli, analyzes the difficulties of realizing the necessary non-perturbative terms (e.g., D7-tadpoles, threshold corrections), and shows how D3-brane gaugino condensation can lift flat directions in models without CSM, offering a path toward fully stabilized Minkowski vacua in a controlled string-theory setting.

Abstract

Supersymmetric Minkowski vacua in IIB orientifold compactifications based on orbifolds with background fluxes and non-perturbative superpotentials are investigated. Especially, microscopic requirements and difficulties to obtain such vacua are discussed. We show that orbifold models with one and two complex structure moduli and supersymmetric 2-form flux can be successfully stabilized to such vacua. By taking additional gaugino condensation on fixed space-time filling D3-branes into account also models without complex structure can be consistently stabilized to Minkowski vacua.

Figures (2)

• Figure 1: Left: T moduli in dependence of $N_c$ for $\Theta=1.2$ (red line), $\Theta=3$ (green line), $\Theta=9$ (blue line). Right: T moduli in dependence of $\Theta$ for $N_c=5$ (red line), $N_c=10$ (green line), $N_c=15$ (blue line).
• Figure 2: Slides of the F-Term scalar potential for models without complex structure, Kählerpotential as in (\ref{['RACEeq11']}), racetrack potential (without 2-form flux) and D3 brane gaugino condensation. Left: V with Kähler moduli fixed at $t\approx T^0$ (V is multiplied by $10^{8}$), Right: V with axion-dilaton fixed at $s\approx S^0$ (V is multiplied by $10^{16}$). Choice of parameters as follows: $n=3$, $N_c=14$, $N_d=15$, $N_e=2$, $C=3$, $D=1$, $F=1$, $\alpha_2\approx 0.072$.