N= 4 chern-simons theories and wrapped M-branes in their gravity duals

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 taking account of D3-brane creation due to the 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, i.e., M5-branes wrapped on 3-cycles. The relation between the fractional brane charge and the torsion of the 3-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 gauge invariance cannot be imposed on all the operators corresponding to wrapped M-branes in the ACIS4/CFT3 correspondence.