Fractional M2-branes

Abstract

We consider two generalizations of the = 6 superconformal Chern-Simons-matter theories with gauge group U(N) × U(N). The first generalization is to = 6 superconformal U(M) × U(N) theories, and the second to = 5 superconformal O(2M) × USp(2N) and O(2M+1) × USp(2N) theories. These theories are conjectured to describe M2-branes probing C 4/Z k in the unitary case, and C 4/ k in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as |M-N| fractional M2-branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals. © SISSA 2008.