N=2 SCFT and M Theory on AdS_4 x Q^{1,1,1}

TL;DR

This work analyzes M2 branes at a conical singularity with target $AdS_4 \times Q^{1,1,1}$, identifying the dual 3d $N=2$ SCFT as $SU(N)^3$ with three chiral families. By computing the scalar Laplacian spectrum on $Q^{1,1,1}$, it matches chiral primaries to KK modes and uncovers a protected tower with $\Delta=R$, while baryon-like operators built from $\mathrm{Tr}(ABC)^R$ have dimension $\Delta = N/3$, corresponding to M5 branes on 5-cycles. The paper then analyzes domain walls from M5 branes on 3-cycles and demonstrates that crossing a baryon M5 with a domain-wall M5 induces M2-brane creation, signaling a gauge-group jump across the wall via a Chern–Simons coupling; the Type IIA picture provides an intuitive dual. Overall, the results reinforce the AdS$_4$/CFT$_3$ correspondence for the non-S^7 Sasaki–Einstein manifold $Q^{1,1,1}$ and suggest natural generalizations to other $X_7$ spaces and wrapped-brane configurations.

Abstract

Coincident M2 branes at a conical singularity are related to M theory on AdS_4 x X_7 for an appropriate 7 dimensional Sasaki-Einstein manifold X_7. For X_7=Q^{1,1,1}=(SU(2) x SU(2) x SU(2))/(U(1) x U(1)) which was found sometime ago, the infrared limit of the theory on N M2 branes was constructed recently. It is the SU(N) x SU(N) x SU(N) gauge theories with three series of chiral fields A_i, i=1,2 transforming in the (N, \bar{N},1) representation, B_j, j=1,2 transforming in the (1,N, \bar{N}) representation and C_k, k=1,2 transforming in the (\bar{N},1,N) representation. From the scalar Laplacian of X_7 on the supergravity side, we discuss the spectrum of chiral primary operators of dual N=2 superconformal field theory in 3 dimensions. We study M5 branes wrapped over 5-cycle of X_7 which were identified as (three types of) baryon like operators made out of N chiral fields recently. We consider M5 brane wrapped over 3-cycle of X_7 which plays the role of domain wall in AdS_4. The new aspect arises when baryon like operators(M5 branes wrapped over 5-cycle) cross a domain wall(M5 brane wrapped over 3-cycle), M2 brane between them must be created.