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

TL;DR

This paper explores N=4 quiver Chern-Simons theories and their gravity duals, analyzing fractional brane charges, dual operators, and wrapped M-branes to deepen understanding of AdS4/CFT3 correspondence.

Contribution

It establishes the relationship between fractional D3-brane charges and the homology of dual geometries, linking gauge theory operators with wrapped M-branes.

Findings

Confirmed the agreement between fractional brane charges and 3-cycle homology.

Reproduced degeneracy and conformal dimensions of baryonic operators from gravity.

Discussed the gauge invariance issues of wrapped M-brane operators.

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.