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Volumn 98, Issue 3, 2011, Pages 225-287

Vortex Counting and Lagrangian 3-Manifolds

Author keywords

BPS invariants; conformal field theory; D branes; gauge theory; vortex equations

Indexed keywords


EID: 80855139588     PISSN: 03779017     EISSN: 15730530     Source Type: Journal    
DOI: 10.1007/s11005-011-0531-8     Document Type: Article
Times cited : (284)

References (61)
  • 2
    • 77952552744 scopus 로고    scopus 로고
    • Exact results for perturbative Chern-Simons theory with complex gauge group
    • (arXiv: 0903. 2472)
    • Dimofte, T., Gukov, S., Lenells, J., Zagier, D.: Exact results for perturbative Chern-Simons theory with complex gauge group. Commun. Num. Theor. Phys. 3, 363-443 (2009). http://xxx. lanl. gov/abs/0903. 2472 (arXiv: 0903. 2472).
    • (2009) Commun. Num. Theor. Phys. , vol.3 , pp. 363-443
    • Dimofte, T.1    Gukov, S.2    Lenells, J.3    Zagier, D.4
  • 3
    • 11244326926 scopus 로고    scopus 로고
    • Seiberg-Witten prepotential from instanton counting
    • (hep-th/0206 161v1)
    • Nekrasov, N. A.: Seiberg-Witten prepotential from instanton counting. Adv. Theor. Math. Phys. 7, 831-864 (2004). http://xxx. lanl. gov/abs/hep-th/0206161v1 (hep-th/0206 161v1).
    • (2004) Adv. Theor. Math. Phys. , vol.7 , pp. 831-864
    • Nekrasov, N.A.1
  • 4
    • 77949772019 scopus 로고    scopus 로고
    • Liouville correlation functions from four-dimensional gauge theories
    • (arXiv: 0906. 3219)
    • Alday, L. F., Gaiotto, D., Tachikawa, Y.: Liouville correlation functions from four-dimensional gauge theories. Lett. Math. Phys. 91, 167-197 (2010). http://xxx. lanl. gov/abs/0906. 3219 (arXiv: 0906. 3219).
    • (2010) Lett. Math. Phys. , vol.91 , pp. 167-197
    • Alday, L.F.1    Gaiotto, D.2    Tachikawa, Y.3
  • 5
    • 0031578202 scopus 로고    scopus 로고
    • T ≥ 2 topological gauge theories and D-branes
    • (hep-th/9612143)
    • T ≥ 2 topological gauge theories and D-branes. Nucl. Phys. B 492, 545-590 (1997). http://xxx. lanl. gov/abs/hep-th/9612143 (hep-th/9612143).
    • (1997) Nucl. Phys. B , vol.492 , pp. 545-590
    • Blau, M.1    Thompson, G.2
  • 6
    • 0042543867 scopus 로고    scopus 로고
    • Euclidean SYM theories by time reduction and special holonomy manifolds
    • (hep-th/9706225)
    • Blau, M., Thompson, G.: Euclidean SYM theories by time reduction and special holonomy manifolds. Phys. Lett. B 415, 242-252 (1997). http://xxx. lanl. gov/abs/hep-th/9706225 (hep-th/9706225).
    • (1997) Phys. Lett. B , vol.415 , pp. 242-252
    • Blau, M.1    Thompson, G.2
  • 7
    • 0038722672 scopus 로고
    • Topological quantum field theory
    • Witten E.: Topological quantum field theory. Commun. Math. Phys. 117, 353 (1988).
    • (1988) Commun. Math. Phys. , vol.117 , pp. 353
    • Witten, E.1
  • 8
    • 0030600821 scopus 로고    scopus 로고
    • D-Branes and topological field theories
    • (hep-th/9511222)
    • Bershadsky, M., Vafa, C., Sadov, V.: D-Branes and topological field theories. Nucl. Phys. B 463, 420-434 (1996). http://xxx. lanl. gov/abs/hep-th/9511222 (hep-th/9511222).
    • (1996) Nucl. Phys. B , vol.463 , pp. 420-434
    • Bershadsky, M.1    Vafa, C.2    Sadov, V.3
  • 9
    • 0031582557 scopus 로고    scopus 로고
    • Geometric engineering of quantum field theories
    • (hep-th/9609239v2)
    • Katz, S., Klemm, A., Vafa, C.: Geometric engineering of quantum field theories. Nucl. Phys. B 497 (1997). http://xxx. lanl. gov/abs/hep-th/9609239v2 (hep-th/9609239v2).
    • (1997) Nucl. Phys. B , vol.497
    • Katz, S.1    Klemm, A.2    Vafa, C.3
  • 10
    • 65549119645 scopus 로고    scopus 로고
    • Gauge theory, ramification, and the geometric Langlands program
    • (hep-th/0612073v2)
    • Gukov, S., Witten, E.: Gauge theory, ramification, and the geometric Langlands program. Curr. Devel. Math. 2006, 35-180 (2008). http://xxx. lanl. gov/abs/hep-th/0612073v2 (hep-th/0612073v2).
    • (2008) Curr. Devel. Math. , vol.2006 , pp. 35-180
    • Gukov, S.1    Witten, E.2
  • 12
  • 16
    • 0000386310 scopus 로고
    • Gauge theory for embedded surfaces, I
    • Kronheimer P. B., Mrowka T. S.: Gauge theory for embedded surfaces, I. Topology 32(4), 773-826 (1993).
    • (1993) Topology , vol.32 , Issue.4 , pp. 773-826
    • Kronheimer, P.B.1    Mrowka, T.S.2
  • 17
    • 0003182749 scopus 로고
    • Gauge theory for embedded surfaces, II
    • Kronheimer P. B., Mrowka T. S.: Gauge theory for embedded surfaces, II. Topology 34(1), 37-97 (1995).
    • (1995) Topology , vol.34 , Issue.1 , pp. 37-97
    • Kronheimer, P.B.1    Mrowka, T.S.2
  • 18
    • 33644894637 scopus 로고    scopus 로고
    • Instanton counting via affine Lie algebras. I. Equivariant J-functions of (affine) flag manifolds and Whittaker vectors
    • CRM Proc. Lecture Notes, Amer. Math. Soc., Providence
    • Braverman, A.: Instanton counting via affine Lie algebras. I. Equivariant J-functions of (affine) flag manifolds and Whittaker vectors. In: Algebraic Structures and Moduli Spaces. CRM Proc. Lecture Notes, vol. 38, pp. 113-132. Amer. Math. Soc., Providence (2004).
    • (2004) Algebraic Structures and Moduli Spaces , vol.38 , pp. 113-132
    • Braverman, A.1
  • 20
    • 0031234520 scopus 로고    scopus 로고
    • Solutions of four-dimensional field theories via M theory
    • (hep-th/9703166v1)
    • Witten, E.: Solutions of four-dimensional field theories via M theory. Nucl. Phys. B 500(3), (1997). http://xxx. lanl. gov/abs/hep-th/9703166v1 (hep-th/9703166v1).
    • (1997) Nucl. Phys. B , vol.500 , Issue.3
    • Witten, E.1
  • 22
    • 11244337480 scopus 로고    scopus 로고
    • ABCD of instantons
    • (hep-th/0404225v2)
    • Nekrasov, N., Shadchin, S.: ABCD of instantons. Commun. Math. Phys. 253, 359-391 (2004). http://xxx. lanl. gov/abs/hep-th/0404225v2 (hep-th/0404225v2).
    • (2004) Commun. Math. Phys. , vol.253 , pp. 359-391
    • Nekrasov, N.1    Shadchin, S.2
  • 27
    • 0010022959 scopus 로고
    • Phases of N = 2 theories in two dimensions
    • Witten E.: Phases of N = 2 theories in two dimensions. Nucl. Phys. B 403(1-2), 159-222 (1993).
    • (1993) Nucl. Phys. B , vol.403 , Issue.1-2 , pp. 159-222
    • Witten, E.1
  • 28
    • 21844486554 scopus 로고
    • Quantum cohomology of flag manifolds and toda lattices
    • (hep-th/9312096v1)
    • Givental, A., Kim, B.: Quantum cohomology of flag manifolds and toda lattices. Commun. Math. Phys. 168, 609-642 (1995). http://xxx. lanl. gov/abs/hep-th/9312096v1 (hep-th/9312096v1).
    • (1995) Commun. Math. Phys. , vol.168 , pp. 609-642
    • Givental, A.1    Kim, B.2
  • 29
    • 0037214431 scopus 로고    scopus 로고
    • Quantum K-theory on flag manifolds, finite-difference toda lattices and quantum groups
    • (math/0108105v1)
    • Givental, A., Lee, Y.-P.: Quantum K-theory on flag manifolds, finite-difference toda lattices and quantum groups. Invent. Math. 151, 193-219 (2003). http://xxx. lanl. gov/abs/math/0108105v1 (math/0108105v1).
    • (2003) Invent. Math. , vol.151 , pp. 193-219
    • Givental, A.1    Lee, Y.-P.2
  • 30
    • 43049110656 scopus 로고    scopus 로고
    • Matrix models, geometric engineering and elliptic genera
    • (hep-th/0310272v4)
    • Hollowood, T. J., Iqbal, A., Vafa, C.: Matrix models, geometric engineering and elliptic genera. JHEP 03, 069 (2008). http://xxx. lanl. gov/abs/hep-th/0310272v4 (hep-th/0310272v4).
    • (2008) JHEP , vol.3 , pp. 069
    • Hollowood, T.J.1    Iqbal, A.2    Vafa, C.3
  • 31
    • 0001334059 scopus 로고    scopus 로고
    • Knot Invariants and topological strings
    • (hep-th/9912123v3)
    • Ooguri, H., Vafa, C.: Knot Invariants and topological strings. Nucl. Phys. B 5777, 419-438 (2000). http://xxx. lanl. gov/abs/hep-th/9912123v3 (hep-th/9912123v3).
    • (2000) Nucl. Phys. B , vol.5777 , pp. 419-438
    • Ooguri, H.1    Vafa, C.2
  • 33
    • 13244277682 scopus 로고    scopus 로고
    • The topological vertex
    • (hep-th/0305132v3)
    • Aganagic, M., Klemm, A., Marino, M., Vafa, C.: The topological vertex. Commun. Math. Phys. 254, 425-478 (2005). http://xxx. lanl. gov/abs/hep-th/0305132v3 (hep-th/0305132v3).
    • (2005) Commun. Math. Phys. , vol.254 , pp. 425-478
    • Aganagic, M.1    Klemm, A.2    Marino, M.3    Vafa, C.4
  • 34
    • 0032538735 scopus 로고    scopus 로고
    • Equivalence of geometric engineering and Hanany-Witten via fractional branes
    • (hep-th/9803232)
    • Karch, A., Lust, D., Smith, D. J.: Equivalence of geometric engineering and Hanany-Witten via fractional branes. Nucl. Phys. B 533, 348-372 (1998). http://xxx. lanl. gov/abs/hep-th/9803232 (hep-th/9803232).
    • (1998) Nucl. Phys. B , vol.533 , pp. 348-372
    • Karch, A.1    Lust, D.2    Smith, D.J.3
  • 35
    • 77952957785 scopus 로고    scopus 로고
    • Open BPS wall crossing and M-theory
    • (arXiv: 0911. 5342)
    • Aganagic, M., Yamazaki, M.: Open BPS wall crossing and M-theory. Nucl. Phys. B 834, 258-272 (2010). http://xxx. lanl. gov/abs/0911. 5342 (arXiv: 0911. 5342).
    • (2010) Nucl. Phys. B , vol.834 , pp. 258-272
    • Aganagic, M.1    Yamazaki, M.2
  • 36
    • 0036345114 scopus 로고    scopus 로고
    • Disk instantons, mirror symmetry and the duality web
    • (hep-th/0105045)
    • Aganagic, M., Klemm, A., Vafa, C.: Disk instantons, mirror symmetry and the duality web. Z. Naturforsch. A 57 (2002) 1-28. http://xxx. lanl. gov/abs/hep-th/0105045 (hep-th/0105045).
    • (2002) Z. Naturforsch. A , vol.57 , pp. 1-28
    • Aganagic, M.1    Klemm, A.2    Vafa, C.3
  • 39
    • 0032473044 scopus 로고    scopus 로고
    • Branes and N = 2 theories in two dimensions
    • (hep-th/9707192v2)
    • Hanany, A., Hori, K.: Branes and N = 2 theories in two dimensions. Nucl. Phys. B 513, 119-174 (1998). http://xxx. lanl. gov/abs/hep-th/9707192v2 (hep-th/9707192v2).
    • (1998) Nucl. Phys. B , vol.513 , pp. 119-174
    • Hanany, A.1    Hori, K.2
  • 41
    • 21444437243 scopus 로고    scopus 로고
    • Instanton counting, Macdonald functions and the moduli space of D-branes
    • (hep-th/0502061)
    • Awata, H., Kanno, H.: Instanton counting, Macdonald functions and the moduli space of D-branes. JHEP 05, 039 (2005). http://xxx. lanl. gov/abs/hep-th/0502061 (hep-th/0502061).
    • (2005) JHEP , vol.5 , pp. 39
    • Awata, H.1    Kanno, H.2
  • 42
    • 2942616401 scopus 로고    scopus 로고
    • All loop topological string amplitudes from Chern-Simons theory
    • (hep-th/0206164)
    • Aganagic, M., Marino, M., Vafa, C.: All loop topological string amplitudes from Chern-Simons theory. Commun. Math. Phys. 247, 467-512, (2004). http://xxx. lanl. gov/abs/hep-th/0206164 (hep-th/0206164).
    • (2004) Commun. Math. Phys. , vol.247 , pp. 467-512
    • Aganagic, M.1    Marino, M.2    Vafa, C.3
  • 43
    • 0003267686 scopus 로고
    • Symmetric functions and Hall polynomials
    • 2nd edn. The Clarendon Press/Oxford University Press, New York. With contributions by A. Zelevinsky. Oxford Science Publications
    • Macdonald, I. G.: Symmetric functions and Hall polynomials. In: Oxford Mathematical Monographs, 2nd edn. The Clarendon Press/Oxford University Press, New York (1995). With contributions by A. Zelevinsky. Oxford Science Publications.
    • (1995) Oxford Mathematical Monographs
    • Macdonald, I.G.1
  • 44
    • 79551477568 scopus 로고    scopus 로고
    • Lagrangians for the Gopakumar-Vafa conjecture
    • (math/0201219v2)
    • Taubes, C. H.: Lagrangians for the Gopakumar-Vafa conjecture. Adv. Theor. Math. Phys. 5, 139-163 (2001). http://xxx. lanl. gov/abs/math/0201219v2 (math/0201219v2).
    • (2001) Adv. Theor. Math. Phys. , vol.5 , pp. 139-163
    • Taubes, C.H.1
  • 45
    • 28444442680 scopus 로고    scopus 로고
    • Khovanov-Rozansky homology and topological strings
    • (hep-th/0412243v3)
    • Gukov, S., Schwarz, A., Vafa, C.: Khovanov-Rozansky homology and topological strings. Lett. Math. Phys. 74, 53-74 (2005). http://xxx. lanl. gov/abs/hep-th/0412243v3 (hep-th/0412243v3).
    • (2005) Lett. Math. Phys. , vol.74 , pp. 53-74
    • Gukov, S.1    Schwarz, A.2    Vafa, C.3
  • 46
    • 33749258410 scopus 로고    scopus 로고
    • The superpolynomial for knot homologies
    • (math/0505662v2)
    • Dunfield, N. M., Gukov, S., Rasmussen, J.: The superpolynomial for knot homologies. Exp. Math. 15(2), 129-160 (2006). http://xxx. lanl. gov/abs/math/0505662v2 (math/0505662v2).
    • (2006) Exp. Math. , vol.15 , Issue.2 , pp. 129-160
    • Dunfield, N.M.1    Gukov, S.2    Rasmussen, J.3
  • 47
    • 79551491388 scopus 로고    scopus 로고
    • On the gauge theory/geometry correspondence
    • (hep-th/9811131v1)s
    • Gopakumar, R., Vafa, C.: On the gauge theory/geometry correspondence. Adv. Theor. Math. Phys. 3, 1415-1443 (1999). http://xxx. lanl. gov/abs/hep-th/9811131v1 (hep-th/9811131v1).
    • (1999) Adv. Theor. Math. Phys. , vol.3 , pp. 1415-1443
    • Gopakumar, R.1    Vafa, C.2
  • 49
    • 33947622125 scopus 로고    scopus 로고
    • Wilson loops, geometric transitions and bubbling Calabi-Yau's
    • (hep-th/0612190)
    • Gomis, J., Okuda, T.: Wilson loops, geometric transitions and bubbling Calabi-Yau's. JHEP 02, 083 (2007). http://xxx. lanl. gov/abs/hep-th/0612190 (hep-th/0612190).
    • (2007) JHEP , vol.2 , pp. 83
    • Gomis J.Okuda, T.1
  • 50
    • 34547657615 scopus 로고    scopus 로고
    • D-branes as a bubbling Calabi-Yau
    • (arXiv: 0704. 3080)
    • Gomis, J., Okuda, T.: D-branes as a bubbling Calabi-Yau. JHEP 07, 005, (2007). http://xxx. lanl. gov/abs/0704. 3080 (arXiv: 0704. 3080).
    • (2007) JHEP , vol.7 , pp. 005
    • Gomis, J.1    Okuda, T.2
  • 51
    • 77954660763 scopus 로고    scopus 로고
    • Gauge theory loop operators and Liouville theory
    • (arXiv: 0909. 1105)
    • Drukker, N., Gomis, J., Okuda, T., Teschner, J.: Gauge theory loop operators and Liouville theory. JHEP 02, 057 (2010). http://xxx. lanl. gov/abs/0909. 1105 (arXiv: 0909. 1105).
    • (2010) JHEP , vol.2 , pp. 057
    • Drukker, N.1    Gomis, J.2    Okuda, T.3    Teschner, J.4
  • 53
    • 70350038349 scopus 로고    scopus 로고
    • (arXiv: 0904. 2715)
    • Gaiotto, D.: N = 2 dualities. http://xxx. lanl. gov/abs/0904. 2715 (arXiv: 0904. 2715).
    • N = 2 dualities
    • Gaiotto, D.1
  • 54
    • 70449879686 scopus 로고    scopus 로고
    • N-1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories
    • (arXiv: 0907. 2189)
    • N-1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories. JHEP 11, 002 (2009). http://xxx. lanl. gov/abs/0907. 2189 (arXiv: 0907. 2189).
    • (2009) JHEP , vol.11 , pp. 002
    • Wyllard, N.1
  • 55
    • 77749343662 scopus 로고    scopus 로고
    • N = 2 gauge theories and degenerate fields of Toda theory
    • (arXiv: 0911. 4787)
    • Kanno, S., Matsuo, Y., Shiba, S., Tachikawa, Y.: N = 2 gauge theories and degenerate fields of Toda theory. Phys. Rev. D 81, 046004 (2010). http://xxx. lanl. gov/abs/0911. 4787 (arXiv: 0911. 4787).
    • (2010) Phys. Rev. D , vol.81 , pp. 046004
    • Kanno, S.1    Matsuo, Y.2    Shiba, S.3    Tachikawa, Y.4
  • 57
    • 28144452143 scopus 로고    scopus 로고
    • Topological strings and integrable hierarchies
    • (hep-th/0312085v1)
    • Aganagic, M., Dijkgraaf, R., Klemm, A., Marino, M., Vafa, C.: Topological strings and integrable hierarchies. Commun. Math. Phys. 261, 451-516, (2006). http://xxx. lanl. gov/abs/hep-th/0312085v1 (hep-th/0312085v1).
    • (2006) Commun. Math. Phys. , vol.261 , pp. 451-516
    • Aganagic, M.1    Dijkgraaf, R.2    Klemm, A.3    Marino, M.4    Vafa, C.5
  • 58
    • 60449115833 scopus 로고    scopus 로고
    • Remodeling the B-model
    • (arXiv: 0709. 1453)
    • Bouchard, V., Klemm, A., Marino, M., Pasquetti, S.: Remodeling the B-model. Commun. Math. Phys. 287, 117-178 (2009). http://xxx. lanl. gov/abs/0709. 1453 (arXiv: 0709. 1453).
    • (2009) Commun. Math. Phys. , vol.287 , pp. 117-178
    • Bouchard, V.1    Klemm, A.2    Marino, M.3    Pasquetti, S.4
  • 59
    • 40549138102 scopus 로고    scopus 로고
    • Supersymmetric gauge theories, intersecting branes and free fermions
    • (arXiv: 0709. 4446)
    • Dijkgraaf, R., Hollands, L., Sulkowski, P., Vafa, C. Supersymmetric gauge theories, intersecting branes and free fermions. JHEP 0802, 106 (2008). http://xxx. lanl. gov/abs/0709. 4446 (arXiv: 0709. 4446).
    • (2008) JHEP , vol.802 , pp. 106
    • Dijkgraaf, R.1    Hollands, L.2    Sulkowski, P.3    Vafa, C.4
  • 61
    • 77953265041 scopus 로고    scopus 로고
    • On F-term contribution to effective action
    • (hep-th/0611278)
    • Shadchin, S.: On F-term contribution to effective action. JHEP 08, 052 (2007). http://xxx. lanl. gov/abs/hep-th/0611278 (hep-th/0611278).
    • (2007) JHEP , vol.8 , pp. 052
    • Shadchin, S.1


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