{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T12:45:50Z","timestamp":1775479550749,"version":"3.50.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/2.0"},{"start":{"date-parts":[[2013,1,29]],"date-time":"2013-01-29T00:00:00Z","timestamp":1359417600000},"content-version":"vor","delay-in-days":28,"URL":"https:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. High Energ. Phys."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n          <\/jats:title>\n          <jats:p>We study singularities of algebraic curves associated with 3d <jats:inline-formula>\n              <jats:tex-math>$ \\mathcal{N}=2 $<\/jats:tex-math>\n            <\/jats:inline-formula> theories that have at least one global flavor symmetry. Of particular interest is a class of theories <jats:italic>T<\/jats:italic>\n            <jats:sub>K<\/jats:sub> labeled by knots, whose partition functions package Poincar\u00e9 polynomials of the <jats:italic>S<\/jats:italic>\n            <jats:sup>\n              <jats:italic>r<\/jats:italic>\n            <\/jats:sup> -colored HOMFLY homologies. We derive the defining equation, called the super-<jats:italic>A<\/jats:italic>-polynomial, for algebraic curves associated with many new examples of 3d <jats:inline-formula>\n              <jats:tex-math>$ \\mathcal{N}=2 $<\/jats:tex-math>\n            <\/jats:inline-formula> theories <jats:italic>T<\/jats:italic>\n            <jats:sub>K<\/jats:sub> and study its singularity structure. In particular, we catalog general types of singularities that presumably exist for all knots and propose their physical interpretation. A computation of super-<jats:italic>A<\/jats:italic>-polynomials is based on a derivation of corresponding superpolynomials, which is interesting in its own right and relies solely on a structure of differentials in <jats:italic>S<\/jats:italic>\n            <jats:sup>\n              <jats:italic>r<\/jats:italic>\n            <\/jats:sup>-colored HOMFLY homologies.<\/jats:p>","DOI":"10.1007\/jhep01(2013)175","type":"journal-article","created":{"date-parts":[[2013,1,30]],"date-time":"2013-01-30T04:26:51Z","timestamp":1359520011000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["3d analogs of Argyres-Douglas theories and knot homologies"],"prefix":"10.1007","volume":"2013","author":[{"given":"Hiroyuki","family":"Fuji","sequence":"first","affiliation":[]},{"given":"Sergei","family":"Gukov","sequence":"additional","affiliation":[]},{"given":"Marko","family":"Sto\u0161i\u0107","sequence":"additional","affiliation":[]},{"given":"Piotr","family":"Sulkowski","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,1,29]]},"reference":[{"key":"5512_CR1","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/S0550-3213(97)00323-4","volume":"B 499","author":"O Aharony","year":"1997","unstructured":"O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M. Strassler, Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th\/9703110] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR2","doi-asserted-by":"publisher","first-page":"089","DOI":"10.1007\/JHEP03(2010)089","volume":"03","author":"A Kapustin","year":"2010","unstructured":"A. Kapustin, B. Willett and I. Yaakov, Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter, JHEP\n                  03 (2010) 089 [arXiv:0909.4559] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR3","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1016\/j.nuclphysb.2012.10.005","volume":"B 867","author":"H Fuji","year":"2013","unstructured":"H. Fuji, S. Gukov and P. Sulkowski, Super-A-polynomial for knots and BPS states, Nucl. Phys. B 867 (2013) 506 [arXiv:1205.1515] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR4","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/BF01217730","volume":"121","author":"E Witten","year":"1989","unstructured":"E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].","journal-title":"Commun. Math. Phys."},{"key":"5512_CR5","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s11005-011-0531-8","volume":"98","author":"T Dimofte","year":"2011","unstructured":"T. Dimofte, S. Gukov and L. Hollands, Vortex Counting and Lagrangian 3-manifolds, Lett. Math. Phys. 98 (2011) 225 [arXiv:1006.0977] [INSPIRE].","journal-title":"Lett. Math. Phys."},{"key":"5512_CR6","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/JHEP08(2011)135","volume":"08","author":"Y Terashima","year":"2011","unstructured":"Y. Terashima and M. Yamazaki, SL(2, $ \\mathbb{R} $) Chern-Simons, Liouville and Gauge Theory on Duality Walls, JHEP\n                  08 (2011) 135 [arXiv:1103.5748] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR7","unstructured":"T. Dimofte, D. Gaiotto and S. Gukov, Gauge Theories Labelled by Three-Manifolds, arXiv:1108.4389 [INSPIRE]."},{"key":"5512_CR8","unstructured":"S. Cecotti, C. Cordova and C. Vafa, Braids, Walls and Mirrors, arXiv:1110.2115 [INSPIRE]."},{"key":"5512_CR9","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1007\/s00220-005-1312-y","volume":"255","author":"S Gukov","year":"2005","unstructured":"S. Gukov, Three-dimensional quantum gravity, Chern-Simons theory and the A polynomial, Commun. Math. Phys. 255 (2005) 577 [hep-th\/0306165] [INSPIRE].","journal-title":"Commun. Math. Phys."},{"key":"5512_CR10","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0550-3213(94)90124-4","volume":"B 426","author":"N Seiberg","year":"1994","unstructured":"N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th\/9407087] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR11","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1016\/0550-3213(94)90214-3","volume":"B 431","author":"N Seiberg","year":"1994","unstructured":"N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th\/9408099] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR12","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/0550-3213(95)00281-V","volume":"B 448","author":"PC Argyres","year":"1995","unstructured":"P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th\/9505062] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR13","unstructured":"S. Gukov and M. Stosic, Homological Algebra of Knots and BPS States, arXiv:1112.0030 [INSPIRE]."},{"key":"5512_CR14","doi-asserted-by":"crossref","unstructured":"S. Nawata, P. Ramadevi, Zodinmawia and X. Sun, Super-A-polynomials for Twist Knots, JHEP\n                  11 (2012) 157 [arXiv:1209.1409] [INSPIRE].","DOI":"10.1007\/JHEP11(2012)157"},{"key":"5512_CR15","doi-asserted-by":"publisher","first-page":"014","DOI":"10.1007\/JHEP05(2011)014","volume":"05","author":"N Hama","year":"2011","unstructured":"N. Hama, K. Hosomichi and S. Lee, SUSY Gauge Theories on Squashed Three-Spheres, JHEP\n                  05 (2011) 014 [arXiv:1102.4716] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR16","unstructured":"A. Kapustin and B. Willett, Generalized Superconformal Index for Three Dimensional Field Theories, arXiv:1106.2484 [INSPIRE]."},{"key":"5512_CR17","unstructured":"T. Dimofte, D. Gaiotto and S. Gukov, 3-Manifolds and 3d Indices, arXiv:1112.5179 [INSPIRE]."},{"key":"5512_CR18","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/JHEP08(2012)141","volume":"08","author":"TT Dumitrescu","year":"2012","unstructured":"T.T. Dumitrescu, G. Festuccia and N. Seiberg, Exploring Curved Superspace, JHEP\n                  08 (2012) 141 [arXiv:1205.1115] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR19","first-page":"065015","volume":"D 86","author":"F Benini","year":"2012","unstructured":"F. Benini, T. Nishioka and M. Yamazaki, 4d Index to 3d Index and 2d TQFT, Phys. Rev. D 86 (2012) 065015 [arXiv:1109.0283] [INSPIRE].","journal-title":"Phys. Rev."},{"key":"5512_CR20","doi-asserted-by":"publisher","first-page":"008","DOI":"10.1007\/JHEP08(2011)008","volume":"08","author":"J Kallen","year":"2011","unstructured":"J. Kallen, Cohomological localization of Chern-Simons theory, JHEP\n                  08 (2011) 008 [arXiv:1104.5353] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR21","first-page":"105018","volume":"D 86","author":"K Ohta","year":"2012","unstructured":"K. Ohta and Y. Yoshida, Non-Abelian Localization for Supersymmetric Yang-Mills- Chern-Simons Theories on Seifert Manifold, Phys. Rev. D 86 (2012) 105018 [arXiv:1205.0046] [INSPIRE].","journal-title":"Phys. Rev."},{"key":"5512_CR22","unstructured":"T. Dimofte, Holomorphic Blocks and Stokes Phenomena, talk given at String Math 2012 conference, Bonn, Germany, 16 July 2012, http:\/\/www.hcm.uni-bonn.de\/events\/eventpages\/ 2012\/string-math-2012\/schedule\/#c3491."},{"key":"5512_CR23","doi-asserted-by":"publisher","first-page":"070","DOI":"10.1007\/JHEP02(2012)070","volume":"02","author":"S Gukov","year":"2012","unstructured":"S. Gukov and P. Sulkowski, A-polynomial, B-model and Quantization, JHEP\n                  02 (2012) 070 [arXiv:1108.0002] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR24","unstructured":"G. Borot and B. Eynard, All-order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials, arXiv:1205.2261 [INSPIRE]."},{"key":"5512_CR25","unstructured":"N.A. Nekrasov and S.L. Shatashvili, Quantization of Integrable Systems and Four Dimensional Gauge Theories, arXiv:0908.4052 [INSPIRE]."},{"key":"5512_CR26","doi-asserted-by":"publisher","first-page":"019","DOI":"10.1007\/JHEP11(2012)019","volume":"11","author":"M Aganagic","year":"2012","unstructured":"M. Aganagic, M.C. Cheng, R. Dijkgraaf, D. Krefl and C. Vafa, Quantum Geometry of Refined Topological Strings, JHEP\n                  11 (2012) 019 [arXiv:1105.0630] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR27","unstructured":"R. Dijkgraaf, Quantum Geometry of Refined Topological Strings, talk given at Simons Summer Workshop in Mathematics and Physics (2011), http:\/\/media.scgp.stonybrook.edu\/ video\/video.php?f=20110804 1 qtp.mp4."},{"key":"5512_CR28","unstructured":"T. Dimofte, Quantum Riemann Surfaces in Chern-Simons Theory, arXiv:1102.4847 [INSPIRE]."},{"key":"5512_CR29","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/S0550-3213(97)80030-2","volume":"B 492","author":"A Hanany","year":"1997","unstructured":"A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th\/9611230] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR30","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0550-3213(97)00444-6","volume":"B 502","author":"J de Boer","year":"1997","unstructured":"J. de Boer, K. Hori, Y. Oz and Z. Yin, Branes and mirror symmetry in N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 502 (1997) 107 [hep-th\/9702154] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR31","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0550-3213(97)00416-1","volume":"B 500","author":"E Witten","year":"1997","unstructured":"E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th\/9703166] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR32","unstructured":"H. Fuji, S. Gukov, P. Sulkowski and H. Awata, Volume Conjecture: Refined and Categorified, arXiv:1203.2182 [INSPIRE]."},{"key":"5512_CR33","unstructured":"M. Aganagic and C. Vafa, Large-N Duality, Mirror Symmetry and a Q-deformed A-polynomial for Knots, arXiv:1204.4709 [INSPIRE]."},{"key":"5512_CR34","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1002\/prop.200610385","volume":"55","author":"S Gukov","year":"2007","unstructured":"S. Gukov, Gauge theory and knot homologies, Fortsch. Phys. 55 (2007) 473 [arXiv:0706.2369] [INSPIRE].","journal-title":"Fortsch. Phys."},{"key":"5512_CR35","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/S0550-3213(97)00282-4","volume":"B 497","author":"SH Katz","year":"1997","unstructured":"S.H. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173 [hep-th\/9609239] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR36","unstructured":"N.M. Dunfield, S. Gukov and J. Rasmussen, The Superpolynomial for knot homologies, math\/0505662 [INSPIRE]."},{"key":"5512_CR37","unstructured":"P. Dunin-Barkowski, A. Mironov, A. Morozov, A. Sleptsov and A. Smirnov, Superpolynomials for toric knots from evolution induced by cut-and-join operators, arXiv:1106.4305 [INSPIRE]."},{"key":"5512_CR38","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/JHEP07(2012)131","volume":"07","author":"H Itoyama","year":"2012","unstructured":"H. Itoyama, A. Mironov, A. Morozov and A. Morozov, HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations, JHEP\n                  07 (2012) 131 [arXiv:1203.5978] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR39","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/BF01231526","volume":"118","author":"D Cooper","year":"1994","unstructured":"D. Cooper, M. Culler, H. Gillet, D. Long and P. B. Shalen, Plane curves associated to character varieties of 3-manifolds, Invent. Math. 118 (1994) 47","journal-title":"Invent. Math."},{"key":"5512_CR40","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1215\/S0012-7094-08-14125-0","volume":"141","author":"L Ng","year":"2008","unstructured":"L. Ng, Framed knot contact homology, Duke Math. J. 141 (2008) 365 [math\/0407071].","journal-title":"Duke Math. J."},{"key":"5512_CR41","doi-asserted-by":"publisher","first-page":"247","DOI":"10.2140\/gt.2005.9.247","volume":"9","author":"L Ng","year":"2005","unstructured":"L. Ng, Knot and braid invariants from contact homology I, Geom. Topol. 9 (2005) 247. [math\/0302099].","journal-title":"Geom. Topol."},{"key":"5512_CR42","doi-asserted-by":"publisher","first-page":"1603","DOI":"10.2140\/gt.2005.9.1603","volume":"9","author":"L Ng","year":"2005","unstructured":"L. Ng, Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil, Geom. Topol. 9 (2005) 1603 [math\/0303343].","journal-title":"Geom. Topol"},{"key":"5512_CR43","doi-asserted-by":"publisher","first-page":"2189","DOI":"10.1016\/j.aim.2011.04.014","volume":"227","author":"L Ng","year":"2011","unstructured":"L. Ng, Combinatorial knot contact homology and transverse knots, Adv. Math. 227 (2011) 2189 [arXiv:1010.0451].","journal-title":"Adv. Math."},{"key":"5512_CR44","unstructured":"L. Ng, Mathematica notebook, (2012), http:\/\/www.math.duke.edu\/\u02dcng\/math\/Augmentation Polynomials.nb."},{"key":"5512_CR45","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/0550-3213(95)00671-0","volume":"B 461","author":"PC Argyres","year":"1996","unstructured":"P.C. Argyres, M.R. Plesser, N. Seiberg and E. Witten, New N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 461 (1996) 71 [hep-th\/9511154] [INSPIRE].","journal-title":"Nucl. Phys."},{"key":"5512_CR46","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.aim.2003.05.001","volume":"186","author":"P Ozsvath","year":"2004","unstructured":"P. Ozsvath and Z. Szabo, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 [math\/0209056].","journal-title":"Adv. Math."},{"key":"5512_CR47","unstructured":"J. Rasmussen, Floer homology and knot complements, math\/0306378."},{"key":"5512_CR48","unstructured":"P. Ozsvath and Z. Szabo, Knot Floer homology, genus bounds and mutation, math\/0303225."},{"key":"5512_CR49","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/s11005-005-0008-8","volume":"74","author":"S Gukov","year":"2005","unstructured":"S. Gukov, A.S. Schwarz and C. Vafa, Khovanov-Rozansky homology and topological strings, Lett. Math. Phys. 74 (2005) 53 [hep-th\/0412243] [INSPIRE].","journal-title":"Lett. Math. Phys."},{"key":"5512_CR50","unstructured":"E. Witten, Fivebranes and Knots, arXiv:1101.3216 [INSPIRE]."},{"key":"5512_CR51","doi-asserted-by":"publisher","first-page":"099","DOI":"10.1007\/JHEP10(2011)099","volume":"10","author":"S Cecotti","year":"2011","unstructured":"S. Cecotti and M. Del Zotto, On Arnold\u2019s 14 \u2018exceptional\u2019 N = 2 superconformal gauge theories, JHEP\n                  10 (2011) 099 [arXiv:1107.5747] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR52","doi-asserted-by":"publisher","first-page":"072","DOI":"10.1007\/JHEP05(2012)072","volume":"05","author":"J Seo","year":"2012","unstructured":"J. Seo and K. Dasgupta, Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N = 2 Gauge Theories with Classical Gauge Groups, JHEP\n                  05 (2012) 072 [arXiv:1203.6357] [INSPIRE].","journal-title":"JHEP"},{"key":"5512_CR53","unstructured":"D. Xie, General Argyres-Douglas Theory, arXiv:1204.2270 [INSPIRE]."},{"key":"5512_CR54","unstructured":"E. Witten, Analytic Continuation Of Chern-Simons Theory, arXiv:1001.2933 [INSPIRE]."}],"container-title":["Journal of High Energy Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP01(2013)175.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/JHEP01(2013)175\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP01(2013)175","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/JHEP01(2013)175.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T21:36:02Z","timestamp":1630532162000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/JHEP01(2013)175"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":54,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["5512"],"URL":"https:\/\/doi.org\/10.1007\/jhep01(2013)175","relation":{},"ISSN":["1029-8479"],"issn-type":[{"value":"1029-8479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]},"assertion":[{"value":"18 September 2012","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 December 2012","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2013","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"175"}}