AdS_4/CFT_3 duals from M2-branes at hypersurface singularities and their deformations

TL;DR

This work constructs a novel AdS4/CFT3 dual pair between three-dimensional N=2 CS-quiver theories and M-theory on AdS4 × V_{5,2}/Z_k, realized through hypersurface singularities X_n and their links Y_n. It shows that the n=1 case recovers ABJM, while n=2 yields a non-toric, strongly coupled SCFT with a clear gravity dual; higher n do not admit AdS4 backgrounds but are studied via Type IIA/IIB brane constructions. The paper develops a rich dictionary: moduli spaces matching X_n/Z_k, chiral primaries corresponding to KK modes on Y_n, and wrapped branes mapping to baryonic operators, with a deformation in the gravity sector tied to a supersymmetric mass term in the field theory that drives confinement and a geometric deformation of X_2 to T^*S^4. It also provides a brane-engineering perspective (Hanany-Witten) to realize field theory dualities and discusses the IR fate, including possible cascades and domain-wall structures, highlighting both the novelty and limitations of these non-toric AdS4/CFT3 examples.

Abstract

We construct three-dimensional N=2 Chern-Simons-quiver theories which are holographically dual to the M-theory Freund-Rubin solutions AdS_4 x V_{5,2}/Z_k (with or without torsion G-flux), where V_{5,2} is a homogeneous Sasaki-Einstein seven-manifold. The global symmetry group of these theories is generically SU(2) x U(1) x U(1)_R, and they are hence non-toric. The field theories may be thought of as the n=2 member of a family of models, labelled by a positive integer n, arising on multiple M2-branes at certain hypersurface singularities. We describe how these models can be engineered via generalized Hanany-Witten brane constructions. The AdS_4 x V_{5,2}/Z_k solutions may be deformed to a warped geometry R^{1,2} x T^* S^4/Z_k, with self-dual G-flux through the four-sphere. We show that this solution is dual to a supersymmetric mass deformation, which precisely modifies the classical moduli space of the field theory to the deformed geometry.

Figures (7)

• Figure 1: The $\mathcal{A}_1$ quiver.
• Figure 2: The Type IIA reduction of M-theory on $X/\mathbb{Z}_k$ on $U(1)_b$ is $C(M_n)$. This geometry may also be viewed as a fibration of $W^{\zeta}_n$ over the $\mathbb{R}_3$ direction, where the size $|\zeta|$ of the exceptional $\mathbb{CP}^1$ depends on the position in $\mathbb{R}_3$. In particular, the conical singularity of $C(M_n)$ is the conical singularity of $W^0_n$ above the origin in $\mathbb{R}_3$. The above schematic picture would be precisely the toric diagram in the case $n=1$ (for $n>1$ the geometry is not toric).
• Figure 3: The Type IIB brane dual of the Type IIA background $\mathbb{R}^{1,2}_{012}\times\mathbb{R}_3\times W^0_n$ with $N$ spacefilling D2-branes. The Type IIB spacetime is flat: $\mathbb{R}^{1,2}_{012}\times\mathbb{R}_3\times S^1_6\times\mathbb{R}_7\times\mathbb{C}^2_{4589}$. There are $N$ D3-branes filling the $\mathbb{R}^{1,2}_{012}$ directions and wrapping the $S^1_6$ circle; they are at the origin in $\mathbb{R}_3$, $\mathbb{R}_7$ and $\mathbb{C}^2_{4589}$. There are two NS5-branes that are spacefilling in $\mathbb{R}^{1,2}_{012}$ and separated by a distance in the $S^1_6$ circle that is given by the period of $B_2$ through the collapsed $\mathbb{CP}^1$ in the T-dual three-fold geometry $W^0_n$; they both sit at the origin in $\mathbb{R}_7$, fill the $\mathbb{R}_3$ direction, and wrap the holomorphic curves $w_1=\pm \mathrm{i} w_0^n$, respectively, in $\mathbb{C}^2_{4589}$ with complex coordinates $w_0,w_1$. These curves intersect at the origin $w_0=w_1=0$. $n=1$ is the standard Hanany-Witten brane configuration for the conifold singularity, where the NS5-branes are linearly embedded.
• Figure 4: On the left hand side: the positions of the two NS5-branes with resolution parameter $\zeta$ in the Type IIA dual. The NS5-brane at position $\zeta$ is that wrapped on $w_1=\mathrm{i} w_0^n$, while the brane at the origin is that wrapped on $w_1=-\mathrm{i} w_0^n$. On the right hand side: the positions of the 5-branes after turning on the RR flux in the Type IIA dual, which fibres the resolution parameter over the $\mathbb{R}_3$ direction. One of the branes rotates so that they now intersect at the origin of the $\mathbb{R}_3-\mathbb{R}_7$ plane.
• Figure 5: On the left hand side: the naive T-dual configuration to a D2-brane wrapped on the $\mathbb{CP}^1$ at a fixed non-zero point in $\mathbb{R}_3$ is a D1-brane stretching between the two NS5-branes, with $k$ fundamental strings also ending on the D1-brane and one of the NS5-branes to cancel the tadpole. On the right hand side: the correct T-dual configuration, in which the D1-brane and $k$ fundamental strings form a $(1,k)$ string bound state, which then must necessarily end on a $(1,k)$5-brane. (Notice that the D1-brane must also wind around the $S^1_6$ circle as one moves from one 5-brane to the other along its worldvolume.)