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T-branes and defects

  • Fernando Marchesano
  • Raffaele SavelliEmail author
  • Sebastian Schwieger
Open Access
Regular Article - Theoretical Physics
  • 16 Downloads

Abstract

We study T-branes on compact Kähler surfaces, in the presence of fields localised at curves. If such fields are treated as defects, their vevs induce delta-function sources for the 7-brane background, possibly leading to profiles with poles. We find that the presence of defect sources relaxes the constraints on globally well-defined T-brane configurations, avoiding the obstruction to building them on surfaces of positive curvature. Profiles with poles can be understood, from a 4d viewpoint, as non-trivial vevs for massive modes induced by the defects, and come with their own set of constraints. In the special case of fields localised on a self-intersection curve, we show how to retrieve the Hitchin system with defects from an ordinary global one with enhanced symmetry.

Keywords

D-branes Supersymmetric Gauge Theory Differential and Algebraic Geometry Superstring Vacua 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    L.E. Ibáñez and A.M. Uranga, String Theory and Particle Physics. An Introduction to String Phenomenology, Cambridge University Press (2012) [INSPIRE].
  2. [2]
    F. Denef, Les Houches Lectures on Constructing String Vacua, Les Houches 87 (2008) 483 [arXiv:0803.1194] [INSPIRE].CrossRefGoogle Scholar
  3. [3]
    J.J. Heckman, Particle Physics Implications of F-theory, Ann. Rev. Nucl. Part. Sci. 60 (2010) 237 [arXiv:1001.0577] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    T. Weigand, Lectures on F-theory compactifications and model building, Class. Quant. Grav. 27 (2010) 214004 [arXiv:1009.3497] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    M. Wijnholt, Higgs Bundles and String Phenomenology, Proc. Symp. Pure Math. 85 (2012) 275 [arXiv:1201.2520] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  6. [6]
    A. Maharana and E. Palti, Models of Particle Physics from Type IIB String Theory and F-theory: A Review, Int. J. Mod. Phys. A 28 (2013) 1330005 [arXiv:1212.0555] [INSPIRE].
  7. [7]
    T. Weigand, TASI Lectures on F-theory, arXiv:1806.01854 [INSPIRE].
  8. [8]
    R. Donagi, S. Katz and E. Sharpe, Spectra of D-branes with Higgs vevs, Adv. Theor. Math. Phys. 8 (2004) 813 [hep-th/0309270] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, Flavor Structure in F-theory Compactifications, JHEP 08 (2010) 036 [arXiv:0910.2762] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    S. Cecotti, C. Cordova, J.J. Heckman and C. Vafa, T-Branes and Monodromy, JHEP 07 (2011) 030 [arXiv:1010.5780] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    R. Donagi and M. Wijnholt, Gluing Branes, I, JHEP 05 (2013) 068 [arXiv:1104.2610] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    N.J. Hitchin, The Selfduality equations on a Riemann surface, Proc. Lond. Math. Soc. 55 (1987) 59 [INSPIRE].CrossRefzbMATHGoogle Scholar
  13. [13]
    R. Donagi and M. Wijnholt, Model Building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theoryI, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
  15. [15]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theoryII: Experimental Predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [INSPIRE].
  16. [16]
    R. Donagi and M. Wijnholt, Breaking GUT Groups in F-theory, Adv. Theor. Math. Phys. 15 (2011) 1523 [arXiv:0808.2223] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    M. Cicoli, F. Quevedo and R. Valandro, de Sitter from T-branes, JHEP 03 (2016) 141 [arXiv:1512.04558] [INSPIRE].
  18. [18]
    C.-C. Chiou, A.E. Faraggi, R. Tatar and W. Walters, T-branes and Yukawa Couplings, JHEP 05 (2011) 023 [arXiv:1101.2455] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    R. Donagi and M. Wijnholt, Gluing Branes II: Flavour Physics and String Duality, JHEP 05 (2013) 092 [arXiv:1112.4854] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    A. Font, F. Marchesano, D. Regalado and G. Zoccarato, Up-type quark masses in SU(5) F-theory models, JHEP 11 (2013) 125 [arXiv:1307.8089] [INSPIRE].
  21. [21]
    L.B. Anderson, J.J. Heckman and S. Katz, T-Branes and Geometry, JHEP 05 (2014) 080 [arXiv:1310.1931] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d Conformal Matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
  23. [23]
    A. Collinucci and R. Savelli, T-branes as branes within branes, JHEP 09 (2015) 161 [arXiv:1410.4178] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    A. Collinucci and R. Savelli, F-theory on singular spaces, JHEP 09 (2015) 100 [arXiv:1410.4867] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    F. Marchesano, D. Regalado and G. Zoccarato, Yukawa hierarchies at the point of E 8 in F-theory, JHEP 04 (2015) 179 [arXiv:1503.02683] [INSPIRE].
  26. [26]
    F. Carta, F. Marchesano and G. Zoccarato, Fitting fermion masses and mixings in F-theory GUTs, JHEP 03 (2016) 126 [arXiv:1512.04846] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    J.J. Heckman, T. Rudelius and A. Tomasiello, 6D RG Flows and Nilpotent Hierarchies, JHEP 07 (2016) 082 [arXiv:1601.04078] [INSPIRE].
  28. [28]
    A. Collinucci, S. Giacomelli, R. Savelli and R. Valandro, T-branes through 3d mirror symmetry, JHEP 07 (2016) 093 [arXiv:1603.00062] [INSPIRE].
  29. [29]
    I. Bena, J. Blabäck, R. Minasian and R. Savelli, There and back again: A T-branes tale, JHEP 11 (2016) 179 [arXiv:1608.01221] [INSPIRE].
  30. [30]
    F. Marchesano and S. Schwieger, T-branes and α -corrections, JHEP 11 (2016) 123 [arXiv:1609.02799] [INSPIRE].
  31. [31]
    N. Mekareeya, T. Rudelius and A. Tomasiello, T-branes, Anomalies and Moduli Spaces in 6D SCFTs, JHEP 10 (2017) 158 [arXiv:1612.06399] [INSPIRE].
  32. [32]
    J.M. Ashfaque, Monodromic T-Branes And The SO(10)GUT , arXiv:1701.05896 [INSPIRE].
  33. [33]
    L.B. Anderson, J.J. Heckman, S. Katz and L.P. Schaposnik, T-Branes at the Limits of Geometry, JHEP 10 (2017) 058 [arXiv:1702.06137] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    I. Bena, J. Blabäck and R. Savelli, T-branes and Matrix Models, JHEP 06 (2017) 009 [arXiv:1703.06106] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    A. Collinucci, S. Giacomelli and R. Valandro, T-branes, monopoles and S-duality, JHEP 10 (2017) 113 [arXiv:1703.09238] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    M. Cicoli, I. Garcìa-Etxebarria, C. Mayrhofer, F. Quevedo, P. Shukla and R. Valandro, Global Orientifolded Quivers with Inflation, JHEP 11 (2017) 134 [arXiv:1706.06128] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    F. Marchesano, R. Savelli and S. Schwieger, Compact T-branes, JHEP 09 (2017) 132 [arXiv:1707.03797] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    L.B. Anderson, M. Esole, L. Fredrickson and L.P. Schaposnik, Singular Geometry and Higgs Bundles in String Theory, SIGMA 14 (2018) 037 [arXiv:1710.08453] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  39. [39]
    F. Apruzzi, J.J. Heckman, D.R. Morrison and L. Tizzano, 4D Gauge Theories with Conformal Matter, JHEP 09 (2018) 088 [arXiv:1803.00582] [INSPIRE].
  40. [40]
    M. Cvetič, J.J. Heckman and L. Lin, Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory, JHEP 11 (2018) 001 [arXiv:1806.10594] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  41. [41]
    J.J. Heckman, T. Rudelius and A. Tomasiello, Fission, Fusion and 6D RG Flows, JHEP 02 (2019) 167 [arXiv:1807.10274] [INSPIRE].
  42. [42]
    F. Apruzzi, F. Hassler, J.J. Heckman and T.B. Rochais, Nilpotent Networks and 4D RG Flows, arXiv:1808.10439 [INSPIRE].
  43. [43]
    F. Carta, S. Giacomelli and R. Savelli, SUSY enhancement from T-branes, JHEP 12 (2018) 127 [arXiv:1809.04906] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin Systems and the WKB Approximation, arXiv:0907.3987 [INSPIRE].
  45. [45]
    A. Font and L.E. Ibáñez, Matter wave functions and Yukawa couplings in F-theory Grand Unification, JHEP 09 (2009) 036 [arXiv:0907.4895] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    S. Cecotti, M.C.N. Cheng, J.J. Heckman and C. Vafa, Yukawa Couplings in F-theory and Non-Commutative Geometry, arXiv:0910.0477 [INSPIRE].
  47. [47]
    H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, More on Dimension-4 Proton Decay Problem in F-theorySpectral Surface, Discriminant Locus and Monodromy, Nucl. Phys. B 840 (2010) 304 [arXiv:1004.3870] [INSPIRE].
  48. [48]
    R. Blumenhagen, V. Braun, T.W. Grimm and T. Weigand, GUTs in Type IIB Orientifold Compactifications, Nucl. Phys. B 815 (2009) 1 [arXiv:0811.2936] [INSPIRE].
  49. [49]
    W. Ballmann, Lectures on Kähler manifolds, ESI Lectures in Mathematics and Physics, European Mathematical Society (2006).Google Scholar
  50. [50]
    J.P. Conlon and E. Palti, Aspects of Flavour and Supersymmetry in F-theory GUTs, JHEP 01 (2010) 029 [arXiv:0910.2413] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    L. Aparicio, A. Font, L.E. Ibáñez and F. Marchesano, Flux and Instanton Effects in Local F-theory Models and Hierarchical Fermion Masses, JHEP 08 (2011) 152 [arXiv:1104.2609] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    A. Font, L.E. Ibáñez, F. Marchesano and D. Regalado, Non-perturbative effects and Yukawa hierarchies in F-theory SU(5) Unification, JHEP 03 (2013) 140 [Erratum ibid. 07 (2013) 036] [arXiv:1211.6529] [INSPIRE].
  53. [53]
    R. Minasian and A. Tomasiello, Variations on stability, Nucl. Phys. B 631 (2002) 43 [hep-th/0104041] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Fernando Marchesano
    • 1
  • Raffaele Savelli
    • 2
    Email author
  • Sebastian Schwieger
    • 1
  1. 1.Instituto de Física Teórica UAM-CSICMadridSpain
  2. 2.Dipartimento di Fisica, Università di Roma “Tor Vergata” & INFN — Sezione di Roma 2RomaItaly

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