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Two-dimensional SCFTs from wrapped branes and c-extremization

  • Francesco Benini
  • Nikolay BobevEmail author
Article

Abstract

We apply c-extremization [1], whose proof we review in full detail, to study twodimensional \( \mathcal{N} \) = (0, 2) superconformal field theories arising from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on four-manifolds. We compute the exact central charges of these theories using anomalies and c-extremization. In all cases we also construct AdS3 supergravity solutions of type IIB and eleven-dimensional supergravity, which are holographic duals to the field theories at large N, and exactly reproduce the central charges computed via c-extremization.

Keywords

Supersymmetric gauge theory Field Theories in Lower Dimensions AdS-CFT Correspondence 

References

  1. [1]
    F. Benini and N. Bobev, Exact two-dimensional superconformal R-symmetry and c-extremization, Phys. Rev. Lett. 110 (2013) 061601 [arXiv:1211.4030] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum Configurations for Superstrings, Nucl. Phys. B 258 (1985) 46 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    D. Gepner, Space-Time Supersymmetry in Compactified String Theory and Superconformal Models, Nucl. Phys. B 296 (1988) 757 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    T. Banks, L.J. Dixon, D. Friedan and E.J. Martinec, Phenomenology and Conformal Field Theory Or Can String Theory Predict the Weak Mixing Angle?, Nucl. Phys. B 299 (1988) 613 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    T.T. Dumitrescu and N. Seiberg, Supercurrents and Brane Currents in Diverse Dimensions, JHEP 07 (2011) 095 [arXiv:1106.0031] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    A. Adams, D. Tong and B. Wecht., unpublished.Google Scholar
  8. [8]
    K.A. Intriligator and B. Wecht, The Exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    C. Closset, T.T. Dumitrescu, G. Festuccia, Z. Komargodski and N. Seiberg, Contact Terms, Unitarity and F-Maximization in Three-Dimensional Superconformal Theories, JHEP 10 (2012) 053 [arXiv:1205.4142] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Bershadsky, A. Johansen, V. Sadov and C. Vafa, Topological reduction of 4 − D SYM to 2 − D σ-models, Nucl. Phys. B 448 (1995) 166 [hep-th/9501096] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].ADSGoogle Scholar
  13. [13]
    A. Almuhairi and J. Polchinski, Magnetic AdS × R 2 : Supersymmetry and stability, arXiv:1108.1213 [INSPIRE].
  14. [14]
    J.A. Harvey, R. Minasian and G.W. Moore, NonAbelian tensor multiplet anomalies, JHEP 09 (1998) 004 [hep-th/9808060] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    L.F. Alday, F. Benini and Y. Tachikawa, Liouville/Toda central charges from M5-branes, Phys. Rev. Lett. 105 (2010) 141601 [arXiv:0909.4776] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    I. Bah, C. Beem, N. Bobev and B. Wecht, AdS/CFT Dual Pairs from M5-Branes on Riemann Surfaces, Phys. Rev. D 85 (2012) 121901 [arXiv:1112.5487] [INSPIRE].ADSGoogle Scholar
  18. [18]
    I. Bah, C. Beem, N. Bobev and B. Wecht, Four-Dimensional SCFTs from M5-Branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    J. Distler and S. Kachru, (0,2) Landau-Ginzburg theory, Nucl. Phys. B 413 (1994) 213 [hep-th/9309110] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    E. Silverstein and E. Witten, Global U(1) R symmetry and conformal invariance of (0,2) models, Phys. Lett. B 328 (1994) 307 [hep-th/9403054] [INSPIRE].MathSciNetADSGoogle Scholar
  21. [21]
    I.V. Melnikov, (0,2) Landau-Ginzburg Models and Residues, JHEP 09 (2009) 118 [arXiv:0902.3908] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].MathSciNetADSGoogle Scholar
  24. [24]
    L. Álvarez-Gaumé and P.H. Ginsparg, The Topological Meaning of Nonabelian Anomalies, Nucl. Phys. B 243 (1984) 449 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    L. Álvarez-Gaumé and P.H. Ginsparg, The Structure of Gauge and Gravitational Anomalies, Annals Phys. 161 (1985) 423 [Erratum ibid. 171 (1986) 233] [INSPIRE].
  26. [26]
    E. Witten, Global Gravitational Anomalies, Commun. Math. Phys. 100 (1985) 197.MathSciNetADSzbMATHCrossRefGoogle Scholar
  27. [27]
    G. ’t Hooft in Recent Developments in Gauge Theories, pg. 135. Plenum, New York (1980), republished in Unity of Forces in the Universe, edited by A. Zee, World Scientific, Singapore (1982), Vol. II, pg. 1004.Google Scholar
  28. [28]
    P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory. Springer-Verlag, New York, (1997).zbMATHCrossRefGoogle Scholar
  29. [29]
    J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge University Press, (1998).Google Scholar
  30. [30]
    P. Spindel, A. Sevrin, W. Troost and A. Van Proeyen, Complex structures on parallelized group manifolds and supersymmetric σ-modelS, Phys. Lett. B 206 (1988) 71 [INSPIRE].ADSGoogle Scholar
  31. [31]
    P. Spindel, A. Sevrin, W. Troost and A. Van Proeyen, Extended Supersymmetric σ-models on Group Manifolds. 1. The Complex Structures, Nucl. Phys. B 308 (1988) 662 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    A. Sevrin, W. Troost, A. Van Proeyen and P. Spindel, Extended supersymmetric σ-modelS on group manifolds. 2. current algebras, Nucl. Phys. B 311 (1988) 465 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    Y. Kazama and H. Suzuki, New N = 2 Superconformal Field Theories and Superstring Compactification, Nucl. Phys. B 321 (1989) 232 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    Y. Kazama and H. Suzuki, Characterization of N = 2 Superconformal Models Generated by Coset Space Method, Phys. Lett. B 216 (1989) 112 [INSPIRE].MathSciNetADSGoogle Scholar
  35. [35]
    C. Hull and B.J. Spence, N = 2 current algebra and coset models, Phys. Lett. B 241 (1990) 357 [INSPIRE].MathSciNetADSGoogle Scholar
  36. [36]
    S. Parkhomenko, Extended superconformal current algebras and finite dimensional Manin triples, Sov. Phys. JETP 75 (1992) 1 [INSPIRE].MathSciNetGoogle Scholar
  37. [37]
    E. Getzler, Manin triples and N = 2 superconformal field theory, hep-th/9307041 [INSPIRE].
  38. [38]
    D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].MathSciNetADSGoogle Scholar
  39. [39]
    V. Dotsenko and V. Fateev, Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models, Nucl. Phys. B 240 (1984) 312 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  40. [40]
    A. Kapustin, Holomorphic reduction of N = 2 gauge theories, Wilson-t Hooft operators and S-duality, hep-th/0612119 [INSPIRE].
  41. [41]
    M. Günaydin, L. Romans and N. Warner, Gauged N = 8 Supergravity in Five-Dimensions, Phys. Lett. B 154 (1985) 268 [INSPIRE].ADSGoogle Scholar
  42. [42]
    M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged N = 8 D = 5 Supergravity, Nucl. Phys. B 259 (1985) 460 [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    M. Günaydin, L. Romans and N. Warner, Compact and Noncompact Gauged Supergravity Theories in Five-Dimensions, Nucl. Phys. B 272 (1986) 598 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    S. Cucu, H. Lü and J.F. Vazquez-Poritz, A Supersymmetric and smooth compactification of M-theory to AdS 5, Phys. Lett. B 568 (2003) 261 [hep-th/0303211] [INSPIRE].ADSGoogle Scholar
  45. [45]
    S. Cucu, H. Lü and J.F. Vazquez-Poritz, Interpolating from AdS(D − 2) × S 2 to AdS(D), Nucl. Phys. B 677 (2004) 181 [hep-th/0304022] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    J.P. Gauntlett and O. Varela, D = 5 SU(2) x U(1) Gauged Supergravity from D = 11 Supergravity, JHEP 02 (2008) 083 [arXiv:0712.3560] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  47. [47]
    M. Naka, Various wrapped branes from gauged supergravities, hep-th/0206141 [INSPIRE].
  48. [48]
    J.P. Gauntlett, O.A. Mac Conamhna, T. Mateos and D. Waldram, New supersymmetric AdS 3 solutions, Phys. Rev. D 74 (2006) 106007 [hep-th/0608055] [INSPIRE].MathSciNetADSGoogle Scholar
  49. [49]
    J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207.MathSciNetADSzbMATHCrossRefGoogle Scholar
  50. [50]
    M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  51. [51]
    M.T. Anderson, C. Beem, N. Bobev and L. Rastelli, Holographic Uniformization, Commun. Math. Phys. 318 (2013) 429 [arXiv:1109.3724] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  52. [52]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and Electric AdS Solutions in String- and M-theory, Class. Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  53. [53]
    M. Cvetič, M. Duff, P. Hoxha, J.T. Liu, H. Lü et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    N. Kim, AdS 3 solutions of IIB supergravity from D3-branes, JHEP 01 (2006) 094 [hep-th/0511029] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    J.P. Gauntlett, N. Kim and D. Waldram, Supersymmetric AdS 3 , AdS 2 and Bubble Solutions, JHEP 04 (2007) 005 [hep-th/0612253] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  56. [56]
    N. Kim, The Backreacted Káhler Geometry of Wrapped Branes, Phys. Rev. D 86 (2012) 067901 [arXiv:1206.1536] [INSPIRE].ADSGoogle Scholar
  57. [57]
    P. Kraus, Lectures on black holes and the AdS 3 /CF T 2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].MathSciNetADSGoogle Scholar
  58. [58]
    K. Jensen, Chiral anomalies and AdS/CMT in two dimensions, JHEP 01 (2011) 109 [arXiv:1012.4831] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    S. Gukov, E. Martinec, G.W. Moore and A. Strominger, Chern-Simons gauge theory and the AdS 3 /CF T 2 correspondence, hep-th/0403225 [INSPIRE].
  60. [60]
    E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351.MathSciNetADSzbMATHCrossRefGoogle Scholar
  61. [61]
    S. Elitzur, G.W. Moore, A. Schwimmer and N. Seiberg, Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory, Nucl. Phys. B 326 (1989) 108 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  62. [62]
    A. D’Adda, A. Davis and P. Di Vecchia, Effective actions in nonabelian theories, Phys. Lett. B 121 (1983) 335 [INSPIRE].ADSGoogle Scholar
  63. [63]
    E. Witten, Nonabelian Bosonization in Two-Dimensions, Commun. Math. Phys. 92 (1984) 455.MathSciNetADSzbMATHCrossRefGoogle Scholar
  64. [64]
    F. Larsen, The Perturbation spectrum of black holes in N = 8 supergravity, Nucl. Phys. B 536 (1998) 258 [hep-th/9805208] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    D. Marolf and S.F. Ross, Boundary Conditions and New Dualities: Vector Fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  66. [66]
    K. Bardakci, E. Rabinovici and B. Saering, String Models with c < 1 Components, Nucl. Phys. B 299 (1988) 151 [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    D.V. Belyaev and P. van Nieuwenhuizen, Rigid supersymmetry with boundaries, JHEP 04 (2008) 008 [arXiv:0801.2377] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    D.S. Berman and D.C. Thompson, Membranes with a boundary, Nucl. Phys. B 820 (2009) 503 [arXiv:0904.0241] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  69. [69]
    E. Ivanov, S. Krivonos and O. Lechtenfeld, Double vector multiplet and partially broken N =4, D = 3 supersymmetry, Phys. Lett. B 487 (2000) 192 [hep-th/0006017] [INSPIRE].MathSciNetADSGoogle Scholar
  70. [70]
    E. Witten, Some comments on string dynamics, hep-th/9507121 [INSPIRE].
  71. [71]
    E. Witten, Five-brane effective action in M-theory, J. Geom. Phys. 22 (1997) 103 [hep-th/9610234] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  72. [72]
    K.A. Intriligator, Anomaly matching and a Hopf-Wess-Zumino term in 6d, N = (2,0) field theories, Nucl. Phys. B 581 (2000) 257 [hep-th/0001205] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  73. [73]
    P. Yi, Anomaly of (2,0) theories, Phys. Rev. D 64 (2001) 106006 [hep-th/0106165] [INSPIRE].ADSGoogle Scholar
  74. [74]
    J.P. Gauntlett and N. Kim, M five-branes wrapped on supersymmetric cycles. 2., Phys. Rev. D 65 (2002) 086003 [hep-th/0109039] [INSPIRE].MathSciNetADSGoogle Scholar
  75. [75]
    J.P. Gauntlett, N. Kim and D. Waldram, M Five-branes wrapped on supersymmetric cycles, Phys. Rev. D 63 (2001) 126001 [hep-th/0012195] [INSPIRE].MathSciNetADSGoogle Scholar
  76. [76]
    J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  77. [77]
    R. Minasian, G.W. Moore and D. Tsimpis, Calabi-Yau black holes and (0,4) σ-models, Commun. Math. Phys. 209 (2000) 325 [hep-th/9904217] [INSPIRE].MathSciNetADSzbMATHGoogle Scholar
  78. [78]
    J.T. Liu and R. Minasian, Black holes and membranes in AdS 7, Phys. Lett. B 457 (1999) 39 [hep-th/9903269] [INSPIRE].MathSciNetADSGoogle Scholar
  79. [79]
    M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged maximally extended supergravity in seven-dimensions, Phys. Lett. B 143 (1984) 103 [INSPIRE].ADSGoogle Scholar
  80. [80]
    H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear K K reduction of 11 − D supergravity on AdS 7 × S 4 and selfduality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [INSPIRE].ADSGoogle Scholar
  81. [81]
    H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistency of the AdS7 × S 4 reduction and the origin of selfduality in odd dimensions, Nucl. Phys. B 581 (2000) 179 [hep-th/9911238] [INSPIRE].ADSCrossRefGoogle Scholar
  82. [82]
    J.P. Gauntlett, O.A. Mac Conamhna, T. Mateos and D. Waldram, AdS spacetimes from wrapped M5 branes, JHEP 11 (2006) 053 [hep-th/0605146] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  83. [83]
    P. Figueras, O.A. Mac Conamhna and E. O Colgain, Global geometry of the supersymmetric AdS 3 /CF T 2 correspondence in M-theory, Phys. Rev. D 76 (2007) 046007 [hep-th/0703275] [INSPIRE].ADSGoogle Scholar
  84. [84]
    O.J. Ganor, Compactification of tensionless string theories, hep-th/9607092 [INSPIRE].
  85. [85]
    F. Benini and S. Cremonesi, Partition functions of N = (2,2) gauge theories on S 2 and vortices, arXiv:1206.2356 [INSPIRE].
  86. [86]
    N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact Results in D = 2 Supersymmetric Gauge Theories, arXiv:1206.2606 [INSPIRE].
  87. [87]
    D.Z. Freedman, M. Headrick and A. Lawrence, On closed string tachyon dynamics, Phys. Rev. D 73 (2006) 066015 [hep-th/0510126] [INSPIRE].MathSciNetADSGoogle Scholar
  88. [88]
    D. Kutasov, New results on thea theoremin four-dimensional supersymmetric field theory, hep-th/0312098 [INSPIRE].
  89. [89]
    Y. Tachikawa, Five-dimensional supergravity dual of a-maximization, Nucl. Phys. B 733 (2006) 188 [hep-th/0507057] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  90. [90]
    P. Szepietowski, Comments on a-maximization from gauged supergravity, JHEP 12 (2012) 018 [arXiv:1209.3025] [INSPIRE].ADSCrossRefGoogle Scholar
  91. [91]
    D. Martelli, J. Sparks and S.-T. Yau, The Geometric dual of a-maximisation for Toric Sasaki-Einstein manifolds, Commun. Math. Phys. 268 (2006) 39 [hep-th/0503183] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  92. [92]
    D. Martelli, J. Sparks and S.-T. Yau, Sasaki-Einstein manifolds and volume minimisation, Commun. Math. Phys. 280 (2008) 611 [hep-th/0603021] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  93. [93]
    J.P. Gauntlett, N. Kim, S. Pakis and D. Waldram, Membranes wrapped on holomorphic curves, Phys. Rev. D 65 (2002) 026003 [hep-th/0105250] [INSPIRE].MathSciNetADSGoogle Scholar
  94. [94]
    F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  95. [95]
    D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  96. [96]
    F. Benini, S. Benvenuti and Y. Tachikawa, Webs of five-branes and N = 2 superconformal field theories, JHEP 09 (2009) 052 [arXiv:0906.0359] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  97. [97]
    D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin Systems and the WKB Approximation, arXiv:0907.3987 [INSPIRE].
  98. [98]
    M. Aganagic, A Stringy Origin of M2 Brane Chern-Simons Theories, Nucl. Phys. B 835 (2010) 1 [arXiv:0905.3415] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  99. [99]
    F. Benini, C. Closset and S. Cremonesi, Chiral flavors and M2-branes at toric CY4 singularities, JHEP 02 (2010) 036 [arXiv:0911.4127] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  100. [100]
    F. Benini, C. Closset and S. Cremonesi, Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3, JHEP 09 (2011) 005 [arXiv:1105.2299] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  101. [101]
    P.H. Ginsparg, Applications Of Topological And Differential Geometric Methods To Anomalies In Quantum Field Theory, in New Perspectives in Quantum Field Theories: proceedings, World Scientific, Singapore, 1985.Google Scholar
  102. [102]
    C.G. Callan Jr. and J.A. Harvey, Anomalies and Fermion Zero Modes on Strings and Domain Walls, Nucl. Phys. B 250 (1985) 427 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  103. [103]
    M. Sohnius, Introducing Supersymmetry, Phys. Rept. 128 (1985) 39 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  104. [104]
    N. Bobev, A. Kundu, K. Pilch and N.P. Warner, Supersymmetric Charged Clouds in AdS5, JHEP 03 (2011) 070 [arXiv:1005.3552] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  105. [105]
    K. Behrndt, A.H. Chamseddine and W. Sabra, BPS black holes in N = 2 five-dimensional AdS supergravity, Phys. Lett. B 442 (1998) 97 [hep-th/9807187] [INSPIRE].MathSciNetADSGoogle Scholar
  106. [106]
    M.T. Anderson, A survey of Einstein metrics on 4-manifolds, arXiv:0810.4830.

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© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Simons Center for Geometry and Physics Stony Brook UniversityStony BrookU.S.A.

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