Quantum corrections to N=2 Chern-Simons theories with flavor and their AdS4 duals

TL;DR

This work develops a Lagrangian framework for ${ m N}=2$ Chern-Simons–matter theories describing M2-branes at Calabi–Yau 4-fold singularities, extended by fundamental flavors from D6 branes. It shows that one-loop monopole corrections and their OPEs determine the quantum-modified moduli space, leading to a precise algebraic description $X=(X_c imesf C^2)//U(1)$ with $t ilde{t}=f^{N_f}$, consistent with the M-theory lift. The authors apply the formalism to explicit examples, including embeddings in ${f CP}^3$, a non-toric $V^{5,2}$, and chiral flavors yielding cones over $Q^{111}$, and connect the field theory data to IIA/IIB brane constructions and AdS$_4$ duals. These results provide a concrete link between 3d flavored CS theories and their holographic geometries, clarifying how D6-branes induce flavor and modify the moduli space. The work thus supplies a robust, geometry-grounded handle on M2-brane theories with flavor and their AdS$_4$ duals.

Abstract

We add fundamental flavors to N=2 Chern-Simons-matter theories living on M2 branes probing a Calabi-Yau four-fold singularity. This is dual, in the 't Hooft limit described by IIA string theory, to the introduction of supersymmetric D6 branes wrapping AdS4 and a 3-cycle of the internal manifold. The resulting Chern-Simons theories remain conformally invariant, corresponding to the fact that the D6 branes lift to pure geometry in M-theory. The determination of the moduli space relies crucially on the 1-loop contributions to charges and OPE's of monopole operators in these field theories. The general picture is determined for non-chiral and chiral flavors, and is illustrated in several examples.

Figures (2)

• Figure 1: Generalized quiver dual to ${\cal N}=4$ AdS$_4 \times S^7/{\mathbb{Z}}_{p m +1}$.
• Figure 2: Quivers with flavor for the D6 brane in $\mathbb{C}\mathbb{P}^3$ and for $V^{5,2}$.