Parameter spaces of massive IIA solutions

TL;DR

This work constructs and analyzes a new class of ${\cal N}=2$ massive IIA AdS$_4$ solutions with internal geometry as an $S^2$-fibration over $S^2\times S^2$, naturally viewed as massive deformations of Sasaki–Einstein reductions from M-theory. The authors develop a detailed Ansatz yielding a three-function ODE system, study regularity and flux quantization, and identify a dense ${\mathbb R}^3$ parameter space whose boundary points generate orbifold or conifold singularities. On the codimension-one locus where the Romans mass vanishes ($F_0=0$), they lift to M-theory to produce the Sasaki–Einstein family ${A^{p,q,r}}$, with explicit toric data and a toric Calabi–Yau cone; special cases recover known spaces such as $Y^{p,k}$ and $Q^{1,1,1}$. In the massive regime, numerical exploration reveals a rich three-parameter landscape of regular solutions connected to a dual Chern–Simons quiver, suggesting a holographic description for both massless and massive branches and highlighting potential extremal transitions and light brane phenomena in this non-Kähler setting.

Abstract

We find a new class of N=2 massive IIA solutions whose internal spaces are S^2 fibrations over S^2 x S^2. These solutions appear naturally as massive deformations of the type IIA reduction of Sasaki-Einstein manifolds in M-theory, including Q^{1,1,1} and Y^{p,k}, and play a role in the AdS4/CFT3 correspondence. We use this example to initiate a systematic study of the parameter space of massive solutions with fluxes. We define and study the natural parameter space of the solutions, which is a certain dense subset of R^3, whose boundaries correspond to orbifold or conifold singularities. On a codimension-one subset of the parameter space, where the Romans mass vanishes, it is possible to perform a lift to M-theory; extending earlier work, we produce a family A^{p,q,r} of Sasaki-Einstein manifolds with cohomogeneity one and SU(2) x SU(2) x U(1) isometry. We also propose a Chern-Simons theory describing the duals of the massless and massive solutions.

Figures (5)

• Figure 1: The allowed values for the parameters $(q_1,\tilde{q}_1)$. Points in the interior of the diagram correspond to non--singular spaces. Generic points on the boundary correspond to manifolds with a ${\Bbb Z}_2$ orbifold singularity. The points $(\pm 4, \mp 4)$ correspond to spaces with the topology of ${\Bbb C}{\Bbb P}^3/{\Bbb Z}_2$. The points $(\pm\frac{4}{\sqrt{3}},\pm\frac{4}{\sqrt{3}})$ correspond to spaces with a conifold$/{\Bbb Z}_2$ singularity.
• Figure 2: The toric diagram for $A^{p,q,r}$. For $p=q$ we obtain the manifolds $Y^{r,p}\left ( {\Bbb C}\mathbb{P}^1\times {\Bbb C}\mathbb{P}^1\right )$.
• Figure 3: The allowed values for the parameters $(q_1,\tilde{q}_1, \phi_1)$ are the ones in the interior of this diagram. The intersection of this picture with the $\phi_1$ plane is the diagram in figure \ref{['fig:ab']}. A generic point on the boundary represents a manifold with a local ${\Bbb Z}_2$ singularity. Points on the thick black line represent manifolds with a conifold$/{\Bbb Z}_2$ singularity. The "ridge" at $q_1=\tilde{q}_1$ represents spaces with the topology of ${\Bbb C}{\Bbb P}^3/{\Bbb Z}_2$. The point at the very top, which lies at the intersection of the ridge and the black line, represents a space that has two conifold$/{\Bbb Z}_2$ singularities.
• Figure 4: The quiver and Tiling for $A^{p,q,r}$.
• Figure 5: The light region corresponds to the Sasaki--Einstein manifolds whose dual quiver is the one in figure \ref{['fig:tal']}.