Localized O6-plane solutions with Romans mass

TL;DR

This work addresses the existence of localized O6-plane solutions in massive IIA with Romans mass, where the lack of an 11D lift complicates the standard M-theory resolution. Using generalized complex geometry, the authors show that a consistent SU(3)×SU(3) structure near a single O6 allows a perturbative deformation in the Romans mass parameter $F_0$, with the Bianchi identity for $F_4$ following from the constancy of $F_0$. They then construct a full, localized massive O6 solution by combining a first-order deformation with a detailed numerical analysis, finding that the Romans mass removes the unphysical hole around the O6 source and yields a smooth interior, while the massless limit is recovered as $F_0\to 0$ and $\mu\to 0$. The results support the existence of bona fide localized O6 backgrounds in massive IIA and shed light on the structure of AdS4/Minkowski compactifications in this context. Overall, the paper demonstrates that massive IIA admits localized O6 configurations with the unphysical region resolved by Romans mass, contrasting with the smeared solutions and providing a concrete handle on nonperturbative string backgrounds in the presence of $F_0$.

Abstract

Orientifold solutions have an unphysical region around their source; for the O6, the singularity is resolved in M-theory by the Atiyah-Hitchin metric. Massive IIA, however, does not admit an eleven-dimensional lift, and one wonders what happens to the O6 there. In this paper, we find evidence for the existence of localized (unsmeared) O6 solutions in presence of Romans mass, in the context of four-dimensional compactifications. As a first step, we show that for generic supersymmetric compactifications, the Bianchi identity for the F_4 RR field follows from constancy of F_0. Using this, we find a procedure to deform any O6-D6 Minkowski compactification at first order in F_0. For a single O6, some of the symmetries of the massless solution are broken, but what is left is still enough to obtain a system of ODEs with as many variables as equations. Numerical analysis indicates that Romans mass makes the unphysical region disappear.

Figures (1)

• Figure 1: Comparison between the massless O6 solution and a solution with Romans mass. The solid line is $e^A$; the dotted line is $e^\phi$; the dashed lines are $j_3$ (positive) and $a_0$ (negative). On the left we plot these coefficients (in string units, for $g_s=0.1$) for the solution with $F_0=0$: from (\ref{['eq:o6metric']}) and (\ref{['eq:JOO6']}) we get $e^A=(1-r_0/r)^{-1/4}$, $j_3=1/r^2$, $a_0=-1/r$. In particular, the solution diverges at $r=r_0=0.1\,l_s$. On the right, we plot the same coefficients for a supersymmetric solution with localized O6 source, for $\mu\sim .055$, $F_0=\frac{4}{2\pi l_s}$. $j_3$ and $a_0$ retain a power-law behavior, while $e^A$ no longer diverges at $r_0=0.1$. At larger distances, one can see deviations from the flat-space behavior, due to the fact that flat space is not a solution for $F_0\neq0$, as observed earlier.