Open string multi-branched and Kahler potentials

TL;DR

The work analyzes how open string moduli from D-branes couple to RR-flux–generated F-term potentials in type II Calabi–Yau orientifolds, uncovering discrete shift symmetries that tie open moduli to RR flux quanta and yield a multi-branched vacuum structure. By computing the open-closed potential via Minkowski four-forms in type IIA with D6-branes and introducing dressed fluxes, the authors show how open moduli enter the superpotential and scalar potential on equal footing with closed-string sectors. They derive holomorphic variable redefinitions that keep track of open-closed mixing, demonstrate the non-factorisation of the Kahler potential, and reproduce the full F-term potential within 4d ${\cal N}=1$ supergravity, including a DBI contribution from worldvolume fluxes. The framework generalizes to type IIB with D7-branes and Wilson lines, suggesting a unified treatment of open-closed moduli with potential applications to moduli stabilisation, axion monodromy, inflation, and discrete flavour symmetries.

Abstract

We consider type II string compactifications on Calabi-Yau orientifolds with fluxes and D-branes, and analyse the F-term scalar potential that simultaneously involves closed and open string modes. In type IIA models with D6-branes such potential can be directly computed by integrating out Minkowski three-forms. The result shows a multi-branched structure along the space of lifted open string moduli, in which discrete shifts in special Lagrangian and Wilson line deformations are compensated by changes in the RR flux quanta. The same sort of discrete shift symmetries are present in the superpotential and constrain the Kahler potential. As for the latter, inclusion of open string moduli breaks the factorisation between complex structure and Kahler moduli spaces. Nevertheless, the 4d Kahler metrics display a set of interesting relations that allow to rederive the scalar potential analytically. Similar results hold for type IIB flux compactifications with D7-brane Wilson lines.

Figures (1)

• Figure 1: Geometric representation of the orientifold $(T^2\times K3)/\Omega_p (-)^{F_L} {\cal R}$ in terms of factorised two-tori. The red points $1,2,3$ and $4$ correspond to the ${\mathbb Z}_2$ fixed points, while the green dashed lines indicate the fixed planes under the anti-holomorphic involution ${\cal R}$. The torus wrapping numbers for the three-cycles $\Pi_a$, $\Pi_b$ and $\Pi_c$ are given in equation (\ref{['Eq:D6ModelT2K3']}) and the factorisation of $T^4/{\mathbb Z}_2$ has been chosen to easily depict $\Pi_c^{\rm bulk}$.