A note on the holography of Chern-Simons matter theories with flavour

TL;DR

The paper develops a holographic picture for a three-dimensional ${ m N}=3$ Chern-Simons-matter theory with $2N_f$ fundamental flavours, identifying a dual description in M-theory as $N$ M2-branes at the origin of a hypertoric eight-manifold ${ m M}_8$ and analyzing a quenched-flavour regime via D6-branes in ${ m AdS}_4\times{ m CP}^3$. It explicitly constructs the hypertoric geometry, matches its isometries to the field theory’s global symmetries, and demonstrates a stable, supersymmetric D6-brane embedding on ${ m AdS}_4\times{ m CP}^3$ by wrapping ${ m RP}^3$, thereby supporting the flavour sector holographically in the probe limit. The work also discusses symmetry enhancements in the absence of flavours and outlines the challenges of obtaining the full backreacted geometry and a complete operator spectrum. Overall, the paper extends holographic ABJM with fundamental matter and provides concrete geometric and brane-theory constructions to connect bulk and boundary data in 2+1 dimensions.

Abstract

We study a three-dimensional N=3 U(N)_k x U(N)_{-k} Chern-Simons matter theory with flavour, corresponding to the N=6 Aharony-Bergman-Jafferis-Maldacena CSM theory coupled to 2N_f fundamental fields. The dual holographic description is given by the near-horizon geometry of N M2-branes at a particular hypertoric geometry M_8. We explicitly construct the space M_8 and match its isometries to the global symmetries of the field theory. We also discuss the model in the quenched approximation by embedding probe D6-branes in AdS_4 x CP^3.

Figures (3)

• Figure 1: Quiver diagram of the Chern-Simons-Yang-Mills theory with flavours.
• Figure 2: Type IIB brane setup of ABJM plus two stacks of $N_f$ "flavour" D5-branes before (lhs.) and after the web deformation (rhs.).
• Figure 3: Three types of 5-branes in $\mathbb{E}^6$.