N = 2 conformal field theories from M2-branes at conifold singularities

TL;DR

This work investigates how to realize $\mathcal{N}=2$ superconformal field theories in three dimensions from M2-branes at conical singularities, focusing on seven-dimensional coset horizons that yield AdS$_4$ duals. It employs toric geometry to construct the Calabi–Yau cones $C(H)$ for the cones over $Q^{111}$ and $M^{110}$, and analyzes related orbifold singularities $\mathbb{C}^4/(\mathbb{Z}_2)$-type, including their partial resolutions; a double projection from M-theory to Type IIA via a D2–D6 system is discussed to derive the low-energy gauge theories, with surviving fields determined by representations of a discrete group $\Gamma'$, though the explicit SCFT Lagrangian is left for future work. The results lay out concrete toric data and embedding equations for the cones and outline a framework to compare the KK spectrum on AdS$_4\times H^7$ with CFT data, contributing to the AdS$_4$/CFT$_3$ dictionary for $\mathcal{N}=2$ theories.

Abstract

We make some comments on the derivation of N=2 super-conformal field theories with smooth gauge group from M2-branes placed at conifold singularities, giving a detailed prescription for two specific examples: the singular cones over the Q^{111} and M^{110} manifolds.