2015/12/31 by Masazumi Honda
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane #Combinatorics #Cosmology and Gravitation Theories #Gauge group #Gauge theory #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Partition (number theory) #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Quiver #Supersymmetry #hep-th
paper · pdf · doi:10.1007/jhep06(2016)123
18+11 pages, 5 figures; v5: typos corrected
arxiv created 2016/05/13 · openalex publication_date 2016/06/01 · arxiv updated 2016/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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 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 \widehatD -type quiver theories and this leads an interesting relation between certain U(N ) and USp(2N ) supersymmetric gauge theories.