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This theory is the natural generalization of the $\\mathcal{N}=5$ ABJM theory with the gauge group $O(2N+1)_{2k} \\times USp(2N)_{-k}$. 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("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.04335","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-14T14:28:47Z","cross_cats_sorted":[],"title_canon_sha256":"8e4be1f8ca978f2b0f73fe42314932d18827d82fd8dd96358d8952cce7924abe","abstract_canon_sha256":"4027a7dafbb2fd3cff145ddd0b39bbcb459397ec8f1d7de89cadbc1537a9aa2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:51.757773Z","signature_b64":"6h3TGHxAH+0SXcWLp9nLNIqQaDiisYny+OTIAS4bEEw+7un/tZ3/jrZ1BvpzflvTkIDtjCiDrNp2elqIe8WiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"477f56dfd1794b97188f57bda71ca98ab3fed1ec73aa302194119a456b44a171","last_reissued_at":"2026-05-18T01:10:51.757279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:51.757279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact relations between M2-brane theories with and without Orientifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Masazumi Honda","submitted_at":"2015-12-14T14:28:47Z","abstract_excerpt":"We study partition functions of low-energy effective theories of M2-branes, whose type IIB brane constructions include orientifolds. 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