Exact relations between M2-brane theories with and without Orientifolds

Masazumi Honda

doi:10.1007/JHEP06(2016)123

paper

Exact relations between M2-brane theories with and without Orientifolds

arXiv:1512.04335 · doi:10.1007/JHEP06(2016)123

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 $O (2 N + 1) \times U S p (2 N) \times \dots \times O (2 N + 1) \times U S p (2 N)$ . This theory is the natural generalization of the $N = 5$ ABJM theory with the gauge group $O (2 N + 1)_{2 k} \times U S p (2 N)_{- k}$ . 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 $U (N) \times \dots \times U (N)$ . By using this relation, we determine an exact form of the grand partition function of the $O (2 N + 1)_{2} \times U S p (2 N)_{- 1}$ ABJM 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 $U (N + 1)_{4} \times U (N)_{- 4}$ ABJ theory and $U (N)_{2} \times U (N)_{- 2}$ ABJM theory, recently conjectured by Grassi-Hatsuda-Mariño. We also argue that partition functions of $A^_{3}$ quiver 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 $U S p (2 N)$ supersymmetric gauge theories.

18+11 pages, 5 figures; v5: typos corrected

Exact relations between M2-brane theories with and without Orientifolds

Abstract

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