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 S 3, whose gauge group is O(2N + 1) × USp(2N ) × ···×O(2N +1)×USp(2N). This theory is the natural generalization of the \( \mathcal{N} \) = 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 )−1 ABJM theory, where its supersymmetry is expected to be enhanced to \( \mathcal{N} \) = 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 )−4 ABJ theory and U(N )2 × U(N )−2 ABJM theory, recently conjectured by Grassi-Hatsuda-Mariño. We also argue that partition functions of  3 quiver theories have representations in terms of an ideal Fermi gas systems associated with \( \widehat{D} \)-type quiver theories and this leads an interesting relation between certain U(N ) and USp(2N ) supersymmetric gauge theories.
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Honda, M. Exact relations between M2-brane theories with and without orientifolds. J. High Energ. Phys. 2016, 123 (2016). https://doi.org/10.1007/JHEP06(2016)123
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DOI: https://doi.org/10.1007/JHEP06(2016)123