Perturbing gauge/gravity duals by a Romans mass

TL;DR

<3-5 sentences high-level summary describing: The paper develops an algorithmic, first-order perturbation method in the Romans mass $F_0$ to generate massive IIA gravity duals for 3d CFTs, starting from the ${\cal N}=6$ AdS$_4\times\mathbb{CP}^3$ background. It uses generalized complex geometry and a D2-brane probe superpotential as a diagnostic to fix the perturbation and derives explicit ${\cal N}=2$ and ${\cal N}=3$ perturbations, as well as a broader family, including CP$^3$ foliations by ${\rm T}^{11}$ coordinates. The approach directly ties the abelianized superpotential of the field theory to the D2-brane potential and demonstrates an algorithmic workflow for first-order $F_0$ deformations. This yields concrete gravity duals for CS–matter theories with nonzero CS levels and provides a systematic framework for exploring AdS$_4$/CFT$_3$ deformations in massive IIA.

Abstract

We show how to produce algorithmically gravity solutions in massive IIA (as infinitesimal first order perturbations in the Romans mass parameter) dual to assigned conformal field theories. We illustrate the procedure on a family of Chern--Simons--matter conformal field theories that we recently obtained from the N=6 theory by waiving the condition that the levels sum up to zero.