N=4 Chern-Simons theories and wrapped M-branes in their gravity duals

TL;DR

The paper establishes a detailed AdS$_4$/CFT$_3$ dictionary for ${\cal N}=4$ quiver Chern-Simons theories by identifying fractional D3-brane charges with the torsion part of $H_3$ in the dual M-theory geometry $M_{p,q,k}$ and by matching wrapped M5-branes on 5-cycles to baryonic operators with correct dimensions and degeneracies. It generalizes from $k=1$ to arbitrary $k\ge2$, showing how the relevant homology groups transform to $\Gamma/kH$ and how the operator spectrum (including monopole operators) aligns with wrapped-brane configurations. The work also clarifies the status of gauge invariance for baryonic operators in AdS$_4$/CFT$_3$, and relates non-diagonal monopole operators to M2-branes wrapped on 2-cycles, tying the $b_2$ of the internal space to monopole charge structure. Overall, the results sharpen the holographic dictionary for wrapped branes, fractional branes, and monopoles in these ${\cal N}=4$ CS theories and point to further exploration with brane-crystal methods and broader quiver classes.

Abstract

We investigate a class of N=4 quiver Chern-Simons theories and their gravity duals. We define the group of fractional D3-brane charges in a type IIB brane setup with taking account of D3-brane creation due to Hanany-Witten effect, and confirm that it agrees with the 3-cycle homology of the dual geometry, which describes the charges of fractional M2-branes, M5-branes wrapped on 3-cycles. The relation between the fractional brane charge and the torsion of the three-form potential field is partially established. We also discuss the duality between baryonic operators in the Chern-Simons theories and M5-branes wrapped on 5-cycles in the dual geometries. The degeneracy and the conformal dimension of the operators are reproduced on the gravity side. We also comment on the relation between wrapped M2-branes and monopole operators. The baryonic operators we consider are not gauge invariant. We argue that the gauge invariance cannot be imposed on all the operators corresponding to wrapped M-branes in AdS4/CFT3 correspondence.

Figures (7)

• Figure 1: A part of a circular quiver diagram of an ${\cal N}=4$ supersymmetric Chern-Simons theory is shown.
• Figure 2: An example of D3-brane creation process is shown. (a) is an initial configuration consisting of an NS5-brane and a $(k,1)$-fivebrane. If $(k,1)$-brane is moved on the other side of the NS5-brane as shown in (b), $k$ D3-branes are created.
• Figure 3: The orbifold is represented as a fibration over the segment $0\leq t\leq1$.
• Figure 4: The three segments connecting cycles are examples of three types of three-cycles in the orbifold.
• Figure 5: The $\beta$-cycle fibration over the gray disk with the segments removed is an example of unwrapping four-chains.