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Hagedorn-like transition at high supersymmetry breaking scale

  • Hervé Partouche
  • Balthazar de VaulchierEmail author
Open Access
Regular Article - Theoretical Physics
  • 44 Downloads

Abstract

We consider phase transitions occurring in four-dimensional heterotic orbifold models, when the scale of spontaneous breaking of \( \mathcal{N} \) = 1 supersymmetry is of the order of the string scale. The super-Higgs mechanism is implemented by imposing distinct boundary conditions for bosons and fermions along an internal circle of radius R. Depending on the orbifold action, the usual scalars becoming tachyonic when R falls below the Hagedorn radius may or may not be projected out of the spectrum. In all cases, infinitely many other scalars, which are pure Kaluza-Klein or pure winding states along other internal directions, become tachyonic in subregions in moduli space. We derive the off-shell tree level effective potential that takes into account these potentially tachyonic modes. We show that when a combination of the usual tachyons survives the orbifold action, it is the only degree of freedom that actually condenses.

Keywords

Superstrings and Heterotic Strings Supersymmetric Effective Theories Supersymmetry Breaking Tachyon Condensation 

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]
    R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl.3 (1965) 147 [INSPIRE].Google Scholar
  2. [2]
    S. Fubini and G. Veneziano, Level structure of dual-resonance models, Nuovo Cim.A 64 (1969) 811 [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    K. Huang and S. Weinberg, Ultimate temperature and the early universe, Phys. Rev. Lett.25 (1970) 895 [INSPIRE].CrossRefADSGoogle Scholar
  4. [4]
    M. Axenides, S.D. Ellis and C. Kounnas, Universal Behavior of D-dimensional Superstring Models, Phys. Rev.D 37 (1988) 2964 [INSPIRE].ADSMathSciNetGoogle Scholar
  5. [5]
    D. Kutasov and N. Seiberg, Number of degrees of freedom, density of states and tachyons in string theory and CFT, Nucl. Phys.B 358 (1991) 600 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  6. [6]
    B. Sathiapalan, Vortices on the String World Sheet and Constraints on Toral Compactification, Phys. Rev.D 35 (1987) 3277 [INSPIRE].ADSGoogle Scholar
  7. [7]
    Y.I. Kogan, Vortices on the World Sheet and Strings Critical Dynamics, JETP Lett.45 (1987) 709 [Pisma Zh. Eksp. Teor. Fiz.45 (1987) 556] [INSPIRE].
  8. [8]
    J.J. Atick and E. Witten, The Hagedorn Transition and the Number of Degrees of Freedom of String Theory, Nucl. Phys.B 310 (1988) 291 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  9. [9]
    I. Antoniadis and C. Kounnas, Superstring phase transition at high temperature, Phys. Lett.B 261 (1991) 369 [INSPIRE].CrossRefADSGoogle Scholar
  10. [10]
    I. Antoniadis, J.P. Derendinger and C. Kounnas, Nonperturbative temperature instabilities in \( \mathcal{N} \) = 4 strings, Nucl. Phys.B 551 (1999) 41 [hep-th/9902032] [INSPIRE].
  11. [11]
    A. Sen, Universality of the tachyon potential, JHEP12 (1999) 027 [hep-th/9911116] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  12. [12]
    C. Angelantonj, C. Kounnas, H. Partouche and N. Toumbas, Resolution of Hagedorn singularity in superstrings with gravito-magnetic fluxes, Nucl. Phys.B 809 (2009) 291 [arXiv:0808.1357] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  13. [13]
    I. Florakis, C. Kounnas, H. Partouche and N. Toumbas, Non-singular string cosmology in a 2d Hybrid model, Nucl. Phys.B 844 (2011) 89 [arXiv:1008.5129] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  14. [14]
    C. Kounnas, H. Partouche and N. Toumbas, Thermal duality and non-singular cosmology in d-dimensional superstrings, Nucl. Phys.B 855 (2012) 280 [arXiv:1106.0946] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  15. [15]
    C. Kounnas, H. Partouche and N. Toumbas, S-brane to thermal non-singular string cosmology, Class. Quant. Grav.29 (2012) 095014 [arXiv:1111.5816] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  16. [16]
    R.H. Brandenberger, C. Kounnas, H. Partouche, S.P. Patil and N. Toumbas, Cosmological Perturbations Across an S-brane, JCAP03 (2014) 015 [arXiv:1312.2524] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    R. Rohm, Spontaneous Supersymmetry Breaking in Supersymmetric String Theories, Nucl. Phys.B 237 (1984) 553 [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    C. Kounnas and M. Porrati, Spontaneous Supersymmetry Breaking in String Theory, Nucl. Phys.B 310 (1988) 355 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  19. [19]
    S. Ferrara, C. Kounnas and M. Porrati, Superstring Solutions With Spontaneously Broken Four-dimensional Supersymmetry, Nucl. Phys.B 304 (1988) 500 [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    S. Ferrara, C. Kounnas, M. Porrati and F. Zwirner, Superstrings with Spontaneously Broken Supersymmetry and their Effective Theories, Nucl. Phys.B 318 (1989) 75 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  21. [21]
    C. Kounnas and B. Rostand, Coordinate Dependent Compactifications and Discrete Symmetries, Nucl. Phys.B 341 (1990) 641 [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    J.D. Blum and K.R. Dienes, Duality without supersymmetry: The Case of the SO(16) × SO(16) string, Phys. Lett.B 414 (1997) 260 [hep-th/9707148] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  23. [23]
    J.D. Blum and K.R. Dienes, Strong/weak coupling duality relations for nonsupersymmetric string theories, Nucl. Phys.B 516 (1998) 83 [hep-th/9707160] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  24. [24]
    I. Antoniadis, E. Dudas and A. Sagnotti, Supersymmetry breaking, open strings and M-theory, Nucl. Phys.B 544 (1999) 469 [hep-th/9807011] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  25. [25]
    I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti, Partial breaking of supersymmetry, open strings and M-theory, Nucl. Phys.B 553 (1999) 133 [hep-th/9812118] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  26. [26]
    I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti, Open descendants of Z 2× Z 2freely acting orbifolds, Nucl. Phys.B 565 (2000) 123 [hep-th/9907184] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  27. [27]
    J. Scherk and J.H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett.B 82 (1979) 60 [INSPIRE].CrossRefADSGoogle Scholar
  28. [28]
    J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys.B 153 (1979) 61 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  29. [29]
    M. Porrati and F. Zwirner, Supersymmetry Breaking in String Derived Supergravities, Nucl. Phys.B 326 (1989) 162 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  30. [30]
    C. Kounnas and H. Partouche, \( \mathcal{N} \) = 2 → 0 super no-scale models and moduli quantum stability, Nucl. Phys.B 919 (2017) 41 [arXiv:1701.00545] [INSPIRE].
  31. [31]
    W. Siegel, Introduction to string field theory, Adv. Ser. Math. Phys.8 (1988) 1 [hep-th/0107094] [INSPIRE].CrossRefMathSciNetGoogle Scholar
  32. [32]
    E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys.B 268 (1986) 253 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  33. [33]
    N. Berkovits, Pure spinor formalism as an \( \mathcal{N} \) = 2 topological string, JHEP10 (2005) 089 [hep-th/0509120] [INSPIRE].CrossRefADSGoogle Scholar
  34. [34]
    B. Zwiebach, Closed string field theory: Quantum action and the BV master equation, Nucl. Phys.B 390 (1993) 33 [hep-th/9206084] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  35. [35]
    E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos, Naturally Vanishing Cosmological Constant in \( \mathcal{N} \) = 1 Supergravity, Phys. Lett.B 133 (1983) 61 [INSPIRE].CrossRefADSGoogle Scholar
  36. [36]
    E. Cremmer, B. Julia, J. Scherk, S. Ferrara, L. Girardello and P. van Nieuwenhuizen, Spontaneous Symmetry Breaking and Higgs Effect in Supergravity Without Cosmological Constant, Nucl. Phys.B 147 (1979) 105 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  37. [37]
    E. Cremmer, S. Ferrara, L. Girardello and A. Van Proeyen, Yang-Mills Theories with Local Supersymmetry: Lagrangian, Transformation Laws and SuperHiggs Effect, Nucl. Phys.B 212 (1983) 413 [INSPIRE].CrossRefADSGoogle Scholar
  38. [38]
    M. de Roo, Matter Coupling in \( \mathcal{N} \) = 4 Supergravity, Nucl. Phys.B 255 (1985) 515 [INSPIRE].CrossRefADSGoogle Scholar
  39. [39]
    M. de Roo, Gauged \( \mathcal{N} \) = 4 matter couplings, Phys. Lett.B 156 (1985) 331 [INSPIRE].CrossRefADSGoogle Scholar
  40. [40]
    P. Wagemans, Breaking of \( \mathcal{N} \) = 4 Supergravity to \( \mathcal{N} \) = 1, \( \mathcal{N} \) = 2 at Λ = 0, Phys. Lett.B 206 (1988) 241 [INSPIRE].
  41. [41]
    E. Bergshoeff, I.G. Koh and E. Sezgin, Coupling of Yang-Mills to \( \mathcal{N} \) = 4, D = 4 Supergravity, Phys. Lett.B 155 (1985) 71 [INSPIRE].CrossRefADSGoogle Scholar
  42. [42]
    M. de Roo and P. Wagemans, Gauge Matter Coupling in \( \mathcal{N} \) = 4 Supergravity, Nucl. Phys.B 262 (1985) 644 [INSPIRE].CrossRefADSGoogle Scholar
  43. [43]
    J. Schon and M. Weidner, Gauged \( \mathcal{N} \) = 4 supergravities, JHEP05 (2006) 034 [hep-th/0602024] [INSPIRE].CrossRefADSGoogle Scholar
  44. [44]
    E. Kiritsis and C. Kounnas, Perturbative and nonperturbative partial supersymmetry breaking: \( \mathcal{N} \) = 4 → \( \mathcal{N} \) = 2 → \( \mathcal{N} \) = 1, Nucl. Phys.B 503 (1997) 117 [hep-th/9703059] [INSPIRE].
  45. [45]
    T. Coudarchet and H. Partouche, Quantum no-scale regimes and moduli dynamics, Nucl. Phys.B 933 (2018) 134 [arXiv:1804.00466] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  46. [46]
    A. Giveon and M. Porrati, A Completely Duality Invariant Effective Action of \( \mathcal{N} \) = 4 Heterotic Strings, Phys. Lett.B 246 (1990) 54 [INSPIRE].CrossRefADSGoogle Scholar
  47. [47]
    A. Giveon and M. Porrati, Duality invariant string algebra and D = 4 effective actions, Nucl. Phys.B 355 (1991) 422 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  48. [48]
    K.S. Narain, New Heterotic String Theories in Uncompactified Dimensions < 10, Phys. Lett.B 169 (1986) 41 [INSPIRE].
  49. [49]
    K.S. Narain, M.H. Sarmadi and E. Witten, A Note on Toroidal Compactification of Heterotic String Theory, Nucl. Phys.B 279 (1987) 369 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  50. [50]
    A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept.244 (1994) 77 [hep-th/9401139] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  51. [51]
    J. Polchinski, String theory. Volume 2: Superstring theory and beyond, Cambridge University Press (1998).Google Scholar
  52. [52]
    S. Ferrara, L. Girardello, C. Kounnas and M. Porrati, Effective Lagrangians for Four-dimensional Superstrings, Phys. Lett.B 192 (1987) 368 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  53. [53]
    E. Calabi and E. Vesentini, On compact, locally symmetric Kähler manifolds, Ann. Math.71 (1960) 472.CrossRefMathSciNetzbMATHGoogle Scholar
  54. [54]
    S. Ferrara, C. Kounnas, D. Lüst and F. Zwirner, Duality invariant partition functions and automorphic superpotentials for (2, 2) string compactifications, Nucl. Phys.B 365 (1991) 431 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar

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© The Author(s) 2019

Authors and Affiliations

  1. 1.CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de ParisPalaiseauFrance

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