Refined swampland distance conjecture and exotic hybrid Calabi-Yaus

  • David ErkingerEmail author
  • Johanna Knapp
Open Access
Regular Article - Theoretical Physics


We test the refined swampland distance conjecture in the Kähler moduli space of exotic one-parameter Calabi-Yaus. We focus on examples with pseudo-hybrid points. These points, whose properties are not well-understood, are at finite distance in the moduli space. We explicitly compute the lengths of geodesics from such points to the large volume regime and show that the refined swampland distance conjecture holds. To compute the metric we use the sphere partition function of the gauged linear sigma model. We discuss several examples in detail, including one example associated to a gauged linear sigma model with non-abelian gauge group.


Superstring Vacua Supersymmetric Gauge Theory Topological Strings 


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.


  1. [1]
    C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
  2. [2]
    H. Ooguri and C. Vafa, On the geometry of the string landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
  3. [3]
    E. Palti, The Swampland: introduction and review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  4. [4]
    F. Baume and E. Palti, Backreacted axion field ranges in string theory, JHEP 08 (2016) 043 [arXiv:1602.06517] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    D. Klaewer and E. Palti, Super-planckian spatial field variations and quantum gravity, JHEP 01 (2017) 088 [arXiv:1610.00010] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    E. Palti, The weak gravity conjecture and scalar fields, JHEP 08 (2017) 034 [arXiv:1705.04328] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    T.W. Grimm, E. Palti and I. Valenzuela, Infinite distances in field space and massless towers of states, JHEP 08 (2018) 143 [arXiv:1802.08264] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    S.-J. Lee, W. Lerche and T. Weigand, Tensionless strings and the weak gravity conjecture, JHEP 10 (2018) 164 [arXiv:1808.05958] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    S.-J. Lee, W. Lerche and T. Weigand, A stringy test of the scalar weak gravity conjecture, Nucl. Phys. B 938 (2019) 321 [arXiv:1810.05169] [INSPIRE].
  10. [10]
    T.W. Grimm, C. Li and E. Palti, Infinite distance networks in field space and charge orbits, JHEP 03 (2019) 016 [arXiv:1811.02571] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    E. Gonzalo, L.E. Ibáñez and A.M. Uranga, Modular symmetries and the swampland conjectures, JHEP 05 (2019) 105 [arXiv:1812.06520] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  12. [12]
    P. Corvilain, T.W. Grimm and I. Valenzuela, The swampland distance conjecture for Kähler moduli, arXiv:1812.07548 [INSPIRE].
  13. [13]
    M. Scalisi and I. Valenzuela, Swampland distance conjecture, inflation and α-attractors, arXiv:1812.07558 [INSPIRE].
  14. [14]
    S.-J. Lee, W. Lerche and T. Weigand, Modular fluxes, elliptic genera and weak gravity conjectures in four dimensions, arXiv:1901.08065 [INSPIRE].
  15. [15]
    A. Joshi and A. Klemm, Swampland distance conjecture for one-parameter Calabi-Yau threefolds, arXiv:1903.00596 [INSPIRE].
  16. [16]
    F. Marchesano and M. Wiesner, Instantons and infinite distances, arXiv:1904.04848 [INSPIRE].
  17. [17]
    A. Font, A. Herráez and L.E. Ibáñez, The swampland distance conjecture and towers of tensionless branes, arXiv:1904.05379 [INSPIRE].
  18. [18]
    S.-J. Lee, W. Lerche and T. Weigand, Emergent strings, duality and weak coupling limits for two-form fields, arXiv:1904.06344 [INSPIRE].
  19. [19]
    T.W. Grimm and D. Van De Heisteeg, Infinite distances and the axion weak gravity conjecture, arXiv:1905.00901 [INSPIRE].
  20. [20]
    R. Blumenhagen, D. Kläwer, L. Schlechter and F. Wolf, The refined swampland distance conjecture in Calabi-Yau moduli spaces, JHEP 06 (2018) 052 [arXiv:1803.04989] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    R. Blumenhagen, Large field inflation/quintessence and the refined swampland distance conjecture, PoS(CORFU2017)175 [arXiv:1804.10504] [INSPIRE].
  22. [22]
    P.S. Aspinwall and M.R. Plesser, Decompactifications and massless D-branes in hybrid models, JHEP 07 (2010) 078 [arXiv:0909.0252] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
  24. [24]
    H. Jockers et al., Two-sphere partition functions and Gromov-Witten invariants, Commun. Math. Phys. 325 (2014) 1139 [arXiv:1208.6244] [INSPIRE].
  25. [25]
    J. Gomis and S. Lee, Exact Kähler potential from gauge theory and mirror symmetry, JHEP 04 (2013) 019 [arXiv:1210.6022] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  26. [26]
    F. Benini and S. Cremonesi, Partition functions of \( \mathcal{N}=\left(2,2\right) \) gauge theories on S 2 and vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE].
  27. [27]
    N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact results in d = 2 supersymmetric gauge theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].
  28. [28]
    K. Hori and J. Knapp, Linear σ-models with strongly coupled phasesOne parameter models, JHEP 11 (2013) 070 [arXiv:1308.6265] [INSPIRE].
  29. [29]
    J. Halverson, V. Kumar and D.R. Morrison, New methods for characterizing phases of 2D supersymmetric gauge theories, JHEP 09 (2013) 143 [arXiv:1305.3278] [INSPIRE].
  30. [30]
    J. Knapp, M. Romo and E. Scheidegger, Hemisphere partition function and analytic continuation to the conifold point, Commun. Num. Theor. Phys. 11 (2017) 73 [arXiv:1602.01382] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    A. Gerhardus, H. Jockers and U. Ninad, The geometry of gauged linear σ-model correlation functions, Nucl. Phys. B 933 (2018) 65 [arXiv:1803.10253] [INSPIRE].
  32. [32]
    D. van Straten, Calabi-Yau operators, in Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds & Picard-Fuchs equations, L. Ji and S.T. Yau eds., Advanced Lectures in Mathematics volume 42, Int. Press, Somerville U.S.A. (2018).Google Scholar
  33. [33]
    P.S. Aspinwall and M.R. Plesser, General mirror pairs for gauged linear σ-models, JHEP 11 (2015) 029 [arXiv:1507.00301] [INSPIRE].
  34. [34]
    A. Libgober and J. Teitelbaum, Lines on Calabi-Yau complete intersections, mirror symmetry and Picard-Fuchs equations, alg-geom/9301001 [INSPIRE].
  35. [35]
    A. Klemm and S. Theisen, Mirror maps and instanton sums for complete intersections in weighted projective space, Mod. Phys. Lett. A 9 (1994) 1807 [hep-th/9304034] [INSPIRE].
  36. [36]
    C.F. Doran and J.W. Morgan, Mirror symmetry and integral variations of Hodge structure underlying one parameter families of Calabi-Yau threefolds, in the proceedings of the Workshop on Mirror Symmetry 5. Calabi-Yau varieties and mirror symmetry, Dcember 6-1, Banff, Canada (2003).Google Scholar
  37. [37]
    S. Hellerman et al., Cluster decomposition, T-duality and gerby CFTs, Adv. Theor. Math. Phys. 11 (2007) 751 [hep-th/0606034] [INSPIRE].
  38. [38]
    A. Caldararu et al., Non-birational twisted derived equivalences in abelian GLSMs, Commun. Math. Phys. 294 (2010) 605 [arXiv:0709.3855] [INSPIRE].
  39. [39]
    S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, Nucl. Phys. B 433 (1995) 501 [hep-th/9406055] [INSPIRE].
  40. [40]
    A. Klemm, M. Kreuzer, E. Riegler and E. Scheidegger, Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections, JHEP 05 (2005) 023 [hep-th/0410018] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    A. Clingher et al., The 14th case VHS via K3 fibrations, in Recent advances in Hodge theory, M. Kerr ed., London Mathematical Society Lecture Note Series volume 427, Cambridge University Press, Cambridge U.K. (2016).Google Scholar
  42. [42]
    A. Caldararu, J. Knapp and E. Sharpe, GLSM realizations of maps and intersections of Grassmannians and Pfaffians, JHEP 04 (2018) 119 [arXiv:1711.00047] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    A. Kanazawa, Pfaffian Calabi-Yau threefolds and mirror symmetry, Commun. Num. Theor. Phys. 6 (2012) 661 [arXiv:1006.0223].MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    O.N. Zhdanov and A.K. Tsikh, Studying the multiple Mellin-Barnes integrals by means of multidimensional residues, Sib. Math. J. 39 (1998) 245.CrossRefzbMATHGoogle Scholar
  45. [45]
    S. Friot and D. Greynat, On convergent series representations of Mellin-Barnes integrals, J. Math. Phys. 53 (2012) 023508 [arXiv:1107.0328] [INSPIRE].
  46. [46]
    A. Gerhardus and H. Jockers, Dual pairs of gauged linear σ-models and derived equivalences of Calabi-Yau threefolds, J. Geom. Phys. 114 (2017) 223 [arXiv:1505.00099] [INSPIRE].
  47. [47]
    K.J. Larsen and R. Rietkerk, MultivariateResidues: a Mathematica package for computing multivariate residues, Comput. Phys. Commun. 222 (2018) 250 [arXiv:1701.01040] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    E. Sharpe, Predictions for Gromov-Witten invariants of noncommutative resolutions, J. Geom. Phys. 74 (2013) 256 [arXiv:1212.5322] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Mathematical Physics GroupUniversity of ViennaViennaAustria

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