N = 4 Chern - Simons theories and wrapped M 5 - branes in their gravity duals Yosuke Imamura

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 M5branes wrapped on 5-cycles in the dual geometries. The degeneracy and the conformal dimension of the operators are reproduced on the gravity side. The baryonic operators we consider are not gauge invariant. We argue that the gauge invariance of these operators may not be demanded in AdS4/CFT3 correspondence. E-mail: [email protected] E-mail: [email protected]