Skip to main content
SpringerLink
Log in

Quivers as calculators: counting, correlators and Riemann surfaces

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

The spectrum of chiral operators in supersymmetric quiver gauge theories is typically much larger in the free limit, where the superpotential terms vanish. We find that the finite N counting of operators in any free quiver theory, with a product of unitary gauge groups, can be described by associating Young diagrams and Littlewood-Richardson multiplicities to a simple modification of the quiver, which we call the split-node quiver. The large N limit leads to a surprisingly simple infinite product formula for counting gauge invariant operators, valid for any quiver with bifundamental fields. An orthogonal basis for the operators, in the finite N CFT inner product, is given in terms of quiver characters. These are constructed by inserting permutations in the split-node quivers and interpreting the resulting diagrams in terms of symmetric group matrix elements and branching coefficients. The fusion coefficients in the chiral ring - valid both in the UV and in the IR - are computed at finite N. The derivation follows simple diagrammatic moves on the quiver. The large N counting and correlators are expressed in terms of topological field theories on Riemann surfaces obtained by thickening the quiver. The TFTs are based on symmetric groups and defect observables associated with subgroups play an important role. We outline the application of the free field results to the construction of BPS operators in the case of non-zero super-potential.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].

  2. S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  4. M.R. Douglas and G.W. Moore, D-branes, quivers and ALE instantons, hep-th/9603167 [INSPIRE].

  5. J. Pasukonis and S. Ramgoolam, From counting to construction of BPS states in N = 4 SYM, JHEP 02 (2011) 078 [arXiv:1010.1683] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. R. de Mello Koch and S. Ramgoolam, A double coset ansatz for integrability in AdS/CFT, JHEP 06 (2012) 083 [arXiv:1204.2153] [INSPIRE].

    Article  Google Scholar 

  7. J. McGreevy, L. Susskind and N. Toumbas, Invasion of the giant gravitons from Anti-de Sitter space, JHEP 06 (2000) 008 [hep-th/0003075] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. V. Balasubramanian, M. Berkooz, A. Naqvi and M.J. Strassler, Giant gravitons in conformal field theory, JHEP 04 (2002) 034 [hep-th/0107119] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. S. Corley, A. Jevicki and S. Ramgoolam, Exact correlators of giant gravitons from dual N = 4 SYM theory,Adv. Theor. Math. Phys. 5 (2002) 809 [hep-th/0111222] [INSPIRE].

    MathSciNet  Google Scholar 

  10. H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, hep-th/0201253 [INSPIRE].

  12. W. Fulton and J. Harris, Representation theory: a first course, Springer (1991).

  13. A. Bissi, C. Kristjansen, D. Young and K. Zoubos, Holographic three-point functions of giant gravitons, JHEP 06 (2011) 085 [arXiv:1103.4079] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. P. Caputa, R. de Mello Koch and K. Zoubos, Extremal versus Non-Extremal Correlators with Giant Gravitons, JHEP 08 (2012) 143 [arXiv:1204.4172] [INSPIRE].

    Article  ADS  Google Scholar 

  15. H. Lin, Giant gravitons and correlators, JHEP 12 (2012) 011 [arXiv:1209.6624] [INSPIRE].

    Article  ADS  Google Scholar 

  16. D. Berenstein, Shape and holography: studies of dual operators to giant gravitons, Nucl. Phys. B 675 (2003) 179 [hep-th/0306090] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. D. Sadri and M. Sheikh-Jabbari, Giant hedgehogs: spikes on giant gravitons, Nucl. Phys. B 687 (2004) 161 [hep-th/0312155] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. D. Berenstein, D.H. Correa and S.E. Vazquez, Quantizing open spin chains with variable length: an Example from giant gravitons, Phys. Rev. Lett. 95 (2005) 191601 [hep-th/0502172] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. D. Berenstein, D.H. Correa and S.E. Vazquez, A Study of open strings ending on giant gravitons, spin chains and integrability, JHEP 09 (2006) 065 [hep-th/0604123] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. V. Balasubramanian, D. Berenstein, B. Feng and M.-x. Huang, D-branes in Yang-Mills theory and emergent gauge symmetry, JHEP 03 (2005) 006 [hep-th/0411205] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  21. R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons - with Strings Attached (I), JHEP 06 (2007) 074 [hep-th/0701066] [INSPIRE].

    Article  Google Scholar 

  22. R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons - with Strings Attached (II), JHEP 09 (2007) 049 [hep-th/0701067] [INSPIRE].

    Article  Google Scholar 

  23. D. Bekker, R. de Mello Koch and M. Stephanou, Giant Gravitons - with Strings Attached (III), JHEP 02 (2008) 029 [arXiv:0710.5372] [INSPIRE].

    Article  ADS  Google Scholar 

  24. J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. I. Biswas, D. Gaiotto, S. Lahiri and S. Minwalla, Supersymmetric states of N = 4 Yang-Mills from giant gravitons, JHEP 12 (2007) 006 [hep-th/0606087] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. M. Bianchi, F. Dolan, P. Heslop and H. Osborn, N = 4 superconformal characters and partition functions, Nucl. Phys. B 767 (2007) 163 [hep-th/0609179] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. T.W. Brown, P. Heslop and S. Ramgoolam, Diagonal multi-matrix correlators and BPS operators in N = 4 SYM, JHEP 02 (2008) 030 [arXiv:0711.0176] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. T.W. Brown, P. Heslop and S. Ramgoolam, Diagonal free field matrix correlators, global symmetries and giant gravitons, JHEP 04 (2009) 089 [arXiv:0806.1911] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. Y. Kimura and S. Ramgoolam, Branes, anti-branes and brauer algebras in gauge-gravity duality, JHEP 11 (2007) 078 [arXiv:0709.2158] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. R. Bhattacharyya, S. Collins and R. de Mello Koch, Exact Multi-Matrix Correlators, JHEP 03 (2008) 044 [arXiv:0801.2061] [INSPIRE].

    Article  ADS  Google Scholar 

  31. N. Beisert, The complete one loop dilatation operator of N = 4 super Yang-Mills theory, Nucl. Phys. B 676 (2004) 3 [hep-th/0307015] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. A.V. Ryzhov, Quarter BPS operators in N = 4 SYM, JHEP 11 (2001) 046 [hep-th/0109064] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. E. D’Hoker, P. Heslop, P. Howe and A. Ryzhov, Systematics of quarter BPS operators in N = 4 SYM, JHEP 04 (2003) 038 [hep-th/0301104] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  34. Y. Kimura, S. Ramgoolam and D. Turton, Free particles from Brauer algebras in complex matrix models, JHEP 05 (2010) 052 [arXiv:0911.4408] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. Y. Kimura, Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra, JHEP 12 (2009) 044 [arXiv:0910.2170] [INSPIRE].

    Article  ADS  Google Scholar 

  36. Y. Kimura and S. Ramgoolam, Enhanced symmetries of gauge theory and resolving the spectrum of local operators, Phys. Rev. D 78 (2008) 126003 [arXiv:0807.3696] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  37. Y. Kimura, Quarter BPS classified by Brauer algebra, JHEP 05 (2010) 103 [arXiv:1002.2424] [INSPIRE].

    Article  ADS  Google Scholar 

  38. Y. Kimura, Correlation functions and representation bases in free N = 4 Super Yang-Mills, Nucl. Phys. B 865 (2012) 568 [arXiv:1206.4844] [INSPIRE].

    Article  ADS  Google Scholar 

  39. Y. Kimura and H. Lin, Young diagrams, Brauer algebras and bubbling geometries, JHEP 01 (2012) 121 [arXiv:1109.2585] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. N. Beisert, M. Bianchi, J.F. Morales and H. Samtleben, Higher spin symmetry and N = 4 SYM, JHEP 07 (2004) 058 [hep-th/0405057] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. D.J. Gross and W. Taylor, Two-dimensional QCD is a string theory, Nucl. Phys. B 400 (1993) 181 [hep-th/9301068] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. T. Brown, Complex matrix model duality, Phys. Rev. D 83 (2011) 085002 [arXiv:1009.0674] [INSPIRE].

    ADS  Google Scholar 

  43. R. de Mello Koch and S. Ramgoolam, From Matrix Models and Quantum Fields to Hurwitz Space and the absolute Galois Group, arXiv:1002.1634 [INSPIRE].

  44. R. Gopakumar, What is the Simplest Gauge-String Duality?, arXiv:1104.2386 [INSPIRE].

  45. R. Gopakumar and R. Pius, Correlators in the Simplest Gauge-String Duality, JHEP 03 (2013) 175 [arXiv:1212.1236] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. S. Kachru and E. Silverstein, 4 − D conformal theories and strings on orbifolds, Phys. Rev. Lett. 80 (1998) 4855 [hep-th/9802183] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. S. Franco et al., Gauge theories from toric geometry and brane tilings, JHEP 01 (2006) 128 [hep-th/0505211] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. S. Benvenuti, S. Franco, A. Hanany, D. Martelli and J. Sparks, An Infinite family of superconformal quiver gauge theories with Sasaki-Einstein duals, JHEP 06 (2005) 064 [hep-th/0411264] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. T.K. Dey, Exact Large R-charge Correlators in ABJM Theory, JHEP 08 (2011) 066 [arXiv:1105.0218] [INSPIRE].

    Article  ADS  Google Scholar 

  52. R. de Mello Koch, B.A.E. Mohammed, J. Murugan and A. Prinsloo, Beyond the Planar Limit in ABJM, JHEP 05 (2012) 037 [arXiv:1202.4925] [INSPIRE].

    Article  Google Scholar 

  53. B.A.E. Mohammed, Nonplanar Integrability and Parity in ABJ Theory, arXiv:1207.6948 [INSPIRE].

  54. P. Caputa and B.A.E. Mohammed, From Schurs to Giants in ABJ(M), JHEP 01 (2013) 055 [arXiv:1210.7705] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. A. Bissi, C. Kristjansen, A. Martirosyan and M. Orselli, On Three-point Functions in the AdS 4 /CFT 3 Correspondence, JHEP 01 (2013) 137 [arXiv:1211.1359] [INSPIRE].

    Article  ADS  Google Scholar 

  56. F. Cachazo, M.R. Douglas, N. Seiberg and E. Witten, Chiral rings and anomalies in supersymmetric gauge theory, JHEP 12 (2002) 071 [hep-th/0211170] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  57. R. Dijkgraaf and C. Vafa, A Perturbative window into nonperturbative physics, hep-th/0208048 [INSPIRE].

  58. B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn - deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  60. D. Gaiotto, L. Rastelli and S.S. Razamat, Bootstrapping the superconformal index with surface defects, arXiv:1207.3577 [INSPIRE].

  61. H.-C. Kim, S.-S. Kim and K. Lee, 5-dim Superconformal Index with Enhanced En Global Symmetry, JHEP 10 (2012) 142 [arXiv:1206.6781] [INSPIRE].

    Article  ADS  Google Scholar 

  62. S. Collins, Restricted Schur Polynomials and Finite N Counting, Phys. Rev. D 79 (2009) 026002 [arXiv:0810.4217] [INSPIRE].

    ADS  Google Scholar 

  63. F. Dolan, Counting BPS operators in N = 4 SYM, Nucl. Phys. B 790 (2008) 432 [arXiv:0704.1038] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  64. M.R. Douglas, B.R. Greene and D.R. Morrison, Orbifold resolution by D-branes, Nucl. Phys. B 506 (1997) 84 [hep-th/9704151] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  65. R. Bhattacharyya, R. de Mello Koch and M. Stephanou, Exact Multi-Restricted Schur Polynomial Correlators, JHEP 06 (2008) 101 [arXiv:0805.3025] [INSPIRE].

    Article  ADS  Google Scholar 

  66. R. Dijkgraaf and E. Witten, Topological Gauge Theories and Group Cohomology, Commun. Math. Phys. 129 (1990) 393 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  67. A. D’Adda and P. Provero, Two-dimensional gauge theories of the symmetric group S(n) in the large-N limit, Commun. Math. Phys. 245 (2004) 1 [hep-th/0110243] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  68. S. Cordes, G.W. Moore and S. Ramgoolam, Lectures on 2 − D Yang-Mills theory, equivariant cohomology and topological field theories, Nucl. Phys. Proc. Suppl. 41 (1995) 184 [hep-th/9411210] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  69. M. Fukuma, S. Hosono and H. Kawai, Lattice topological field theory in two-dimensions, Commun. Math. Phys. 161 (1994) 157 [hep-th/9212154] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  70. E. Witten, On quantum gauge theories in two-dimensions, Commun. Math. Phys. 141 (1991) 153 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  71. R. de Mello Koch and S. Ramgoolam, Strings from Feynman Graph counting: without large-N, Phys. Rev. D 85 (2012) 026007 [arXiv:1110.4858] [INSPIRE].

    ADS  Google Scholar 

  72. V. Turaev, Homotopy field theory in dimension two and group algebras, math/9910010 [INSPIRE].

  73. G.W. Moore and G. Segal, D-branes and k-theory in 2D topological field theory, hep-th/0609042 [INSPIRE].

  74. P. Cameron, Combinatorics: topics, techniques, algorithms, Cambridge University Press, Cambridge, U.K. (1994).

    MATH  Google Scholar 

  75. S. Cordes, G.W. Moore and S. Ramgoolam, Large-N 2 − D Yang-Mills theory and topological string theory, Commun. Math. Phys. 185 (1997) 543 [hep-th/9402107] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  76. S. Ramgoolam, Wilson loops in 2 − D Yang-Mills: Euler characters and loop equations, Int. J. Mod. Phys. A 11 (1996) 3885 [hep-th/9412110] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  77. A. Recknagel, Permutation branes, JHEP 04 (2003) 041 [hep-th/0208119] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  78. M. Atiyah, Topological quantum field theories, Publications mathématiques de l’I.H. É.S. 68 (1989) 175.

  79. T. Barmeier and C. Schweigert, A Geometric Construction for Permutation Equivariant Categories from Modular Functors, arXiv:1004.1825.

  80. A. Davydov, L. Kong and I. Runkel, Field theories with defects and the centre functor, arXiv:1107.0495 [INSPIRE].

  81. A. Mironov, A. Morozov and S. Natanzon, A Hurwitz theory avatar of open-closed strings, The European Physical Journal C 73 (2013) 2324 [arXiv:1208.5057] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  82. R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Matrix string theory, Nucl. Phys. B 500 (1997) 43 [hep-th/9703030] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  83. M.A. Luty and W. Taylor, Varieties of vacua in classical supersymmetric gauge theories, Phys. Rev. D 53 (1996) 3399 [hep-th/9506098] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  84. A. Hanany and K.D. Kennaway, Dimer models and toric diagrams, hep-th/0503149 [INSPIRE].

  85. S. Franco, A. Hanany, K.D. Kennaway, D. Vegh and B. Wecht, Brane dimers and quiver gauge theories, JHEP 01 (2006) 096 [hep-th/0504110] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  86. A. Butti, D. Forcella, A. Hanany, D. Vegh and A. Zaffaroni, Counting Chiral Operators in Quiver Gauge Theories, JHEP 11 (2007) 092 [arXiv:0705.2771] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  87. S. Benvenuti, B. Feng, A. Hanany and Y.-H. He, Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics, JHEP 11 (2007) 050 [hep-th/0608050] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  88. C.E. Beasley, BPS branes from baryons, JHEP 11 (2002) 015 [hep-th/0207125] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  89. A. Butti, D. Forcella and A. Zaffaroni, Counting BPS baryonic operators in CFTs with Sasaki-Einstein duals, JHEP 06 (2007) 069 [hep-th/0611229] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  90. D. Forcella, A. Hanany and A. Zaffaroni, Baryonic Generating Functions, JHEP 12 (2007) 022 [hep-th/0701236] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  91. D. Giovannoni, J. Murugan and A. Prinsloo, The Giant graviton on AdS 4 xCP 3 - another step towards the emergence of geometry, JHEP 12 (2011) 003 [arXiv:1108.3084] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  92. A. Hamilton, J. Murugan and A. Prinsloo, Lessons from giant gravitons on AdS 5 × T 1,1, JHEP 06 (2010) 017 [arXiv:1001.2306] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  93. A. Hamilton, J. Murugan, A. Prinsloo and M. Strydom, A Note on dual giant gravitons in AdS 4 × CP 3, JHEP 04 (2009) 132 [arXiv:0901.0009] [INSPIRE].

    Article  ADS  Google Scholar 

  94. A. Mikhailov, Giant gravitons from holomorphic surfaces, JHEP 11 (2000) 027 [hep-th/0010206] [INSPIRE].

    Article  ADS  Google Scholar 

  95. J. Bhattacharya and S. Minwalla, Superconformal Indices for N = 6 Chern Simons Theories, JHEP 01 (2009) 014 [arXiv:0806.3251] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  96. Y. Chen and N. Mekareeya, The Hilbert series of U/SU SQCD and Toeplitz Determinants, Nucl. Phys. B 850 (2011) 553 [arXiv:1104.2045] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  97. A. Hanany and N. Mekareeya, Counting Gauge Invariant Operators in SQCD with Classical Gauge Groups, JHEP 10 (2008) 012 [arXiv:0805.3728] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  98. J. Gray, A. Hanany, Y.-H. He, V. Jejjala and N. Mekareeya, SQCD: a Geometric Apercu, JHEP 05 (2008) 099 [arXiv:0803.4257] [INSPIRE].

    Article  ADS  Google Scholar 

  99. N. Jokela, M. Jarvinen and E. Keski-Vakkuri, New results for the SQCD Hilbert series, JHEP 03 (2012) 048 [arXiv:1112.5454] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  100. M.J. Strassler, The Duality cascade, hep-th/0505153 [INSPIRE].

  101. F. Cachazo, N. Seiberg and E. Witten, Chiral rings and phases of supersymmetric gauge theories, JHEP 04 (2003) 018 [hep-th/0303207] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  102. N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757 [hep-th/0104005] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  103. D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  104. O. Aharony, Y.E. Antebi, M. Berkooz and R. Fishman, ’Holey sheets’: pfaffians and subdeterminants as D-brane operators in large-N gauge theories, JHEP 12 (2002) 069 [hep-th/0211152] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  105. P. Caputa, R. de Mello Koch and P. Diaz, A basis for large operators in N = 4 SYM with orthogonal gauge group, JHEP 03 (2013) 041 [arXiv:1301.1560] [INSPIRE].

    Article  ADS  Google Scholar 

  106. E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  107. A. Gadde, E. Pomoni, L. Rastelli and S.S. Razamat, S-duality and 2d Topological QFT, JHEP 03 (2010) 032 [arXiv:0910.2225] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  108. M. Aganagic, A. Klemm, M. Mariño and C. Vafa, The Topological vertex, Commun. Math. Phys. 254 (2005) 425 [hep-th/0305132] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  109. I. Bena, M. Berkooz, J. de Boer, S. El-Showk and D. Van den Bleeken, Scaling BPS Solutions and pure-Higgs States, JHEP 11 (2012) 171 [arXiv:1205.5023] [INSPIRE].

    Article  ADS  Google Scholar 

  110. K. Papadodimas, Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  111. M. Hamermesh, Group theory and its application to physical problems. Dover publications, 1989

Download references

Author information

Authors and Affiliations

  1. School of Physics and Astronomy, Queen Mary, University of London, Mile End Road, London, E1 4NS, U.K.

    Jurgis Pasukonis & Sanjaye Ramgoolam

Authors
  1. Jurgis Pasukonis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanjaye Ramgoolam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jurgis Pasukonis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pasukonis, J., Ramgoolam, S. Quivers as calculators: counting, correlators and Riemann surfaces. J. High Energ. Phys. 2013, 94 (2013). https://doi.org/10.1007/JHEP04(2013)094

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP04(2013)094

Keywords

Search

Navigation