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We systematically classify the BPS equations in terms of the number of supersymmetry and the R-symmetries of the undeformed and mass-deformed ABJM theories. For the undeformed case, we analyze the ${\\cal N}=2$ BPS equations for U(2)$\\times$U(2) gauge symmetry and obtain a coupled differential equation which can be reduced to either Liouville- or Sinh-Gordon-type vortex equations according to the choice of scalar functions. For the mass-deformed case with U($N$)$\\times$U($N$) gauge symmetry, we ob"},"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":"1211.5886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-11-26T08:41:52Z","cross_cats_sorted":[],"title_canon_sha256":"80c96c5b96dcb13914f3a48430c13b3390f8406cad13f9d5becf484d76fe9fa1","abstract_canon_sha256":"b0335a81ba1925b4abbfade7d91b1652d375136763481c774e248754c7438827"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:55.176237Z","signature_b64":"QaTfPyopSQ0UeY/KjS3+uaFVcXxPZGRFQFNwvjfIXeVoC/0FQe8+W+FR/FjPINKWYv8QDsdI4/lvSnxlxpokAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d2c3fbac4b6f5ff7ba5e019c871f3307c9cd680f944169b9fbc0a5745507cb0","last_reissued_at":"2026-05-18T01:52:55.175804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:55.175804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"BPS Vortices, $Q$-balls, and $Q$-vortices in ${\\cal N}=6$} Chern-Simons Matter Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chanju Kim, Gyungchoon Go, Hiroaki Nakajima, O-Kab Kwon, Yoonbai Kim","submitted_at":"2012-11-26T08:41:52Z","abstract_excerpt":"We investigate the vortex-type BPS equations in the ABJM theory without and with mass-deformation. 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