Beyond Twisted Tori

TL;DR

The paper shows that the conventional constraint $\\omega\\,\\omega=0$ for geometrical fluxes in twisted-torus compactifications can be relaxed by introducing Kaluza-Klein 5-brane monopoles and generalized orbifold planes, which source the fluxes and modify the Bianchi identities to $d\\omega+\\omega\\omega=Q_{KK}$. Through T-duality and M-theory uplifts, it relates this to the NSNS $H$-flux BI as $dH+\\omega H=[{\\nu_5}]$ and to the RR BI as $dG^{(2)}+\\omega G^{(2)}=Q_{RR}$, providing a consistent, duality-covariant framework for flux compactifications with localized sources. This clarifies the ten-dimensional origin of a family of $N=4$ gauged supergravities (the DKPZ class) that could not be realized with only standard fluxes and localized sources, by allowing nonzero total KK charge canceled by geometrical fluxes. The work broadens the landscape of moduli-stabilizing vacua, enables new flux+source configurations in type-IIA orientifolds, and suggests avenues for SUSY breaking and generalized-geometric embeddings in string compactifications.

Abstract

Exploiting the fact that Kaluza-Klein monopoles and the associated generalized orbifold planes are sources for geometrical fluxes, omega, we show that the standard constraint omega.omega=0, valid for superstring compactifications on twisted tori, can be consistently relaxed. This leads to novel possibilities for constructing superstring models with fluxes and localized sources, as well as for stabilizing moduli. This also explains the ten-dimensional origin of a family of N=4 gauged supergravities, whose interpretation in type-IIA orientifold compactifications was lacking.