Exact relations between M2-brane theories with and without orientifolds

Abstract

Abstract: We study partition functions of low-energy effective theories of M2-branes, whose type IIB brane constructions include orientifolds. We mainly focus on circular quiver superconformal Chern-Simons theory on S3, whose gauge group is O(2N + 1) × USp(2N) × ···×O(2N +1)×USp(2N). This theory is the natural generalization of the N = 5 ABJM theory with the gauge group O(2N + 1)2k× USp(2N)−k. We find that the partition function of this type of theory has a simple relation to the one of the M2-brane theory without the orientifolds, whose gauge group is U(N) × · · · × U(N). By using this relation, we determine an exact form of the grand partition function of the O(2N +1)2×USp(2N)−1ABJM theory, where its supersymmetry is expected to be enhanced to N = 6. As another interesting application, we discuss that our result gives a natural physical interpretation of a relation between the grand partition functions of the U(N + 1)4× U(N)−4ABJ theory and U(N)2× U(N)−2ABJM theory, recently conjectured by Grassi-Hatsuda-Mariño. We also argue that partition functions of Â3quiver theories have representations in terms of an ideal Fermi gas systems associated with D^ -type quiver theories and this leads an interesting relation between certain U(N) and USp(2N) supersymmetric gauge theories.