Notes on adding D6 branes wrapping RP3 in AdS4 x CP3

TL;DR

This work studies how adding fundamental matter to the ${\cal N}=6$ ABJM theory yields ${\cal N}=3$ Chern-Simons-matter theories and probes their holographic duals. It develops the quantum-corrected hyperk"ahler moduli space, constructs the chiral ring including monopole operators, and matches these structures to M-theory/IIA backgrounds with D6 branes wrapping $\mathbb{R}\mathbb{P}^3$ in $AdS_4\times \mathbb{C}P^3$, with extensions to general ${\cal N}=3$ quivers. Key results include the dimension shifts of monopole operators due to fundamentals, the ADHM description of the Higgs branch as instantons on $\mathbb{C}^2/\mathbb{Z}_n$, and the interpretation of mass/FI deformations as hyperk"ahler resolutions within the holographic setup. The findings illuminate how fundamental matter reshapes operator spectra and gravity duals in ${\cal N}=3$ holography and provide a framework applicable to a broad class of dual pairs.

Abstract

We deform the N=6 Chern Simons theory by adding extra matter hypermultiplets in a fundamental representation of one or both gauge groups. We compute the quantum corrected moduli space. We verify that the holographic dual of the modified theory consists of the usual AdS4 x CP3 background in presence of AdS4 filling D6 branes which wrap RP3 in CP3. We extend the correspondence to a similar modification of more general known N=3 dual pairs