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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl.3 (1965) 147 [INSPIRE].
S. Fubini and G. Veneziano, Level structure of dual-resonance models, Nuovo Cim.A 64 (1969) 811 [INSPIRE].
K. Huang and S. Weinberg, Ultimate temperature and the early universe, Phys. Rev. Lett.25 (1970) 895 [INSPIRE].
M. Axenides, S.D. Ellis and C. Kounnas, Universal Behavior of D-dimensional Superstring Models, Phys. Rev.D 37 (1988) 2964 [INSPIRE].
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].
B. Sathiapalan, Vortices on the String World Sheet and Constraints on Toral Compactification, Phys. Rev.D 35 (1987) 3277 [INSPIRE].
Y.I. Kogan, Vortices on the World Sheet and String’s Critical Dynamics, JETP Lett.45 (1987) 709 [Pisma Zh. Eksp. Teor. Fiz.45 (1987) 556] [INSPIRE].
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].
I. Antoniadis and C. Kounnas, Superstring phase transition at high temperature, Phys. Lett.B 261 (1991) 369 [INSPIRE].
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].
A. Sen, Universality of the tachyon potential, JHEP12 (1999) 027 [hep-th/9911116] [INSPIRE].
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].
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].
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].
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].
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].
R. Rohm, Spontaneous Supersymmetry Breaking in Supersymmetric String Theories, Nucl. Phys.B 237 (1984) 553 [INSPIRE].
C. Kounnas and M. Porrati, Spontaneous Supersymmetry Breaking in String Theory, Nucl. Phys.B 310 (1988) 355 [INSPIRE].
S. Ferrara, C. Kounnas and M. Porrati, Superstring Solutions With Spontaneously Broken Four-dimensional Supersymmetry, Nucl. Phys.B 304 (1988) 500 [INSPIRE].
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].
C. Kounnas and B. Rostand, Coordinate Dependent Compactifications and Discrete Symmetries, Nucl. Phys.B 341 (1990) 641 [INSPIRE].
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].
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].
I. Antoniadis, E. Dudas and A. Sagnotti, Supersymmetry breaking, open strings and M-theory, Nucl. Phys.B 544 (1999) 469 [hep-th/9807011] [INSPIRE].
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].
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].
J. Scherk and J.H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett.B 82 (1979) 60 [INSPIRE].
J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys.B 153 (1979) 61 [INSPIRE].
M. Porrati and F. Zwirner, Supersymmetry Breaking in String Derived Supergravities, Nucl. Phys.B 326 (1989) 162 [INSPIRE].
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].
W. Siegel, Introduction to string field theory, Adv. Ser. Math. Phys.8 (1988) 1 [hep-th/0107094] [INSPIRE].
E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys.B 268 (1986) 253 [INSPIRE].
N. Berkovits, Pure spinor formalism as an \( \mathcal{N} \) = 2 topological string, JHEP10 (2005) 089 [hep-th/0509120] [INSPIRE].
B. Zwiebach, Closed string field theory: Quantum action and the B − V master equation, Nucl. Phys.B 390 (1993) 33 [hep-th/9206084] [INSPIRE].
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].
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].
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].
M. de Roo, Matter Coupling in \( \mathcal{N} \) = 4 Supergravity, Nucl. Phys.B 255 (1985) 515 [INSPIRE].
M. de Roo, Gauged \( \mathcal{N} \) = 4 matter couplings, Phys. Lett.B 156 (1985) 331 [INSPIRE].
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].
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].
M. de Roo and P. Wagemans, Gauge Matter Coupling in \( \mathcal{N} \) = 4 Supergravity, Nucl. Phys.B 262 (1985) 644 [INSPIRE].
J. Schon and M. Weidner, Gauged \( \mathcal{N} \) = 4 supergravities, JHEP05 (2006) 034 [hep-th/0602024] [INSPIRE].
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].
T. Coudarchet and H. Partouche, Quantum no-scale regimes and moduli dynamics, Nucl. Phys.B 933 (2018) 134 [arXiv:1804.00466] [INSPIRE].
A. Giveon and M. Porrati, A Completely Duality Invariant Effective Action of \( \mathcal{N} \) = 4 Heterotic Strings, Phys. Lett.B 246 (1990) 54 [INSPIRE].
A. Giveon and M. Porrati, Duality invariant string algebra and D = 4 effective actions, Nucl. Phys.B 355 (1991) 422 [INSPIRE].
K.S. Narain, New Heterotic String Theories in Uncompactified Dimensions < 10, Phys. Lett.B 169 (1986) 41 [INSPIRE].
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].
A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept.244 (1994) 77 [hep-th/9401139] [INSPIRE].
J. Polchinski, String theory. Volume 2: Superstring theory and beyond, Cambridge University Press (1998).
S. Ferrara, L. Girardello, C. Kounnas and M. Porrati, Effective Lagrangians for Four-dimensional Superstrings, Phys. Lett.B 192 (1987) 368 [INSPIRE].
E. Calabi and E. Vesentini, On compact, locally symmetric Kähler manifolds, Ann. Math.71 (1960) 472.
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].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1903.09116
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Partouche, H., de Vaulchier, B. Hagedorn-like transition at high supersymmetry breaking scale. J. High Energ. Phys. 2019, 155 (2019). https://doi.org/10.1007/JHEP08(2019)155
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2019)155