Abstract
We study the perturbative stability of four settings that arise in String Theory, when dilaton potentials accompany the breaking of Supersymmetry, in the tachyon-free USp(32) and U(32) orientifold models, and also in the heterotic SO(16) × SO(16) model. The first two settings are a family of AdS3 ×S7 vacua of the orientifold models and a family of AdS7 × S3 vacua of the heterotic model, supported by form fluxes, with small world-sheet and string-loop corrections within wide ranges of parameters. In both cases we find some unstable scalar perturbations, as a result of mixings induced by fluxes, confirming for the first class of vacua a previous result. However, in the second class of vacua they only affect the ℓ = 1 modes, so that a ℤ2 projection induced by an overall parity in the internal space suffices to eliminate them, leading to perturbative stability. Moreover, the constant dilaton profiles of these vacua allow one to extend the analysis to generic potentials, thus exploring the possible effects of higher-order corrections, and we exhibit wide nearby regions of perturbative stability. The solutions in the third setting have nine-dimensional Poincaré symmetry. They include regions with large world-sheet or string-loop corrections, but we show that these vacua have no perturbative instabilities. Finally, the last setting concerns cosmological solutions in ten dimensions where the “climbing” phenomenon takes place: they have bounded string-loop corrections but large world-sheet ones close to the initial singularity. In this case we find that perturbations generally decay, but homogeneous tensor modes exhibit an interesting logarithmic growth that signals a breakdown of isotropy. If the Universe then proceeds to lower dimensions, milder potentials from other branes force all perturbations to remain bounded.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory, 2 vols., Cambridge University Press, Cambridge, U.K., (1987).
J. Polchinski, String theory, 2 vols., Cambridge University Press, Cambridge, U.K., (1998).
C.V. Johnson, D-branes, Cambridge University Press, U.S.A., (2003).
B. Zwiebach, A first course in string theory Cambridge University Press, Cambridge, U.K., (2004).
K. Becker, M. Becker and J.H. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press, Cambridge, U.K., (2007).
E. Kiritsis, String theory in a nutshell, Princeton University Press, Princeton, NJ, U.S.A., (2007).
P. West, Introduction to strings and branes, Cambridge University Press, (2012).
D.Z. Freedman, P. van Nieuwenhuizen and S. Ferrara, Progress Toward a Theory of Supergravity, Phys. Rev. D 13 (1976) 3214 [INSPIRE].
S. Deser and B. Zumino, Consistent Supergravity, Phys. Lett. B 62 (1976) 335 [INSPIRE].
For detailed reviews see: D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge, U.K., (2012).
P. Van Nieuwenhuizen, Supergravity, Phys. Rept. 68 (1981) 189 [INSPIRE].
S. Ferrara and A. Sagnotti, Supergravity at 40: Reflections and Perspectives, Riv. Nuovo Cim. 40 (2017) 279 [arXiv:1702.00743] [INSPIRE].
A. Sagnotti, Open Strings and their Symmetry Groups, in NATO Advanced Summer Institute on Nonperturbative Quantum Field Theory (Cargese Summer Institute) Cargese, France, July 16-30, 1987, pp. 521-528, hep-th/0208020 [INSPIRE].
G. Pradisi and A. Sagnotti, Open String Orbifolds, Phys. Lett. B 216 (1989) 59 [INSPIRE].
P. Hořava, Strings on World Sheet Orbifolds, Nucl. Phys. B 327 (1989) 461 [INSPIRE].
P. Hořava, Background Duality of Open String Models, Phys. Lett. B 231 (1989) 251 [INSPIRE].
M. Bianchi and A. Sagnotti, On the systematics of open string theories, Phys. Lett. B 247 (1990) 517 [INSPIRE].
M. Bianchi and A. Sagnotti, Twist symmetry and open string Wilson lines, Nucl. Phys. B 361 (1991) 519 [INSPIRE].
M. Bianchi, G. Pradisi and A. Sagnotti, Toroidal compactification and symmetry breaking in open string theories, Nucl. Phys. B 376 (1992) 365 [INSPIRE].
A. Sagnotti, A note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B 294 (1992) 196 [hep-th/9210127] [INSPIRE].
E. Dudas, Theory and phenomenology of type-I strings and M-theory, Class. Quant. Grav. 17 (2000) R41 [hep-ph/0006190] [INSPIRE].
C. Angelantonj and A. Sagnotti, Open strings, Phys. Rept. 371 (2002) 1 [Erratum ibid. 376 (2003) 407] [hep-th/0204089] [INSPIRE].
S. Sugimoto, Anomaly cancellations in type-I D9-D9 system and the USp(32) string theory, Prog. Theor. Phys. 102 (1999) 685 [hep-th/9905159] [INSPIRE].
I. Antoniadis, E. Dudas and A. Sagnotti, Brane supersymmetry breaking, Phys. Lett. B 464 (1999) 38 [hep-th/9908023] [INSPIRE].
C. Angelantonj, Comments on open string orbifolds with a nonvanishing B(ab), Nucl. Phys. B 566 (2000) 126 [hep-th/9908064] [INSPIRE].
G. Aldazabal and A.M. Uranga, Tachyon free nonsupersymmetric type IIB orientifolds via brane-antibrane systems, JHEP 10 (1999) 024 [hep-th/9908072] [INSPIRE].
C. Angelantonj, I. Antoniadis, G. D’Appollonio, E. Dudas and A. Sagnotti, Type I vacua with brane supersymmetry breaking, Nucl. Phys. B 572 (2000) 36 [hep-th/9911081] [INSPIRE].
E. Dudas and J. Mourad, Consistent gravitino couplings in nonsupersymmetric strings, Phys. Lett. B 514 (2001) 173 [hep-th/0012071] [INSPIRE].
G. Pradisi and F. Riccioni, Geometric couplings and brane supersymmetry breaking, Nucl. Phys. B 615 (2001) 33 [hep-th/0107090] [INSPIRE].
N. Kitazawa, Brane SUSY Breaking and the Gravitino Mass, JHEP 04 (2018) 081 [arXiv:1802.03088] [INSPIRE].
A. Sagnotti, Some properties of open string theories, in Supersymmetry and unification of fundamental interactions. Proceedings, International Workshop, SUSY 95, Palaiseau, France, May 15-19, 1995, pp. 473-484, hep-th/9509080 [INSPIRE].
A. Sagnotti, Surprises in open string perturbation theory, Nucl. Phys. Proc. Suppl. 56B (1997) 332 [hep-th/9702093] [INSPIRE].
L.J. Dixon and J.A. Harvey, String Theories in Ten-Dimensions Without Space-Time Supersymmetry, Nucl. Phys. B 274 (1986) 93 [INSPIRE].
N. Seiberg and E. Witten, Spin Structures in String Theory, Nucl. Phys. B 276 (1986) 272 [INSPIRE].
L. Álvarez-Gaumé, P.H. Ginsparg, G.W. Moore and C. Vafa, An O(16) × O(16) Heterotic String, Phys. Lett. B 171 (1986) 155 [INSPIRE].
J. Mourad and A. Sagnotti, An Update on Brane Supersymmetry Breaking, arXiv:1711.11494 [INSPIRE].
J. Mourad and A. Sagnotti, AdS Vacua from Dilaton Tadpoles and Form Fluxes, Phys. Lett. B 768 (2017) 92 [arXiv:1612.08566] [INSPIRE].
E. Dudas and J. Mourad, Brane solutions in strings with broken supersymmetry and dilaton tadpoles, Phys. Lett. B 486 (2000) 172 [hep-th/0004165] [INSPIRE].
C.G. Callan Jr., E.J. Martinec, M.J. Perry and D. Friedan, Strings in Background Fields, Nucl. Phys. B 262 (1985) 593 [INSPIRE].
R.C. Myers, New Dimensions for Old Strings, Phys. Lett. B 199 (1987) 371 [INSPIRE].
I. Antoniadis, C. Bachas, J.R. Ellis and D.V. Nanopoulos, Cosmological String Theories and Discrete Inflation, Phys. Lett. B 211 (1988) 393 [INSPIRE].
I. Antoniadis, C. Bachas, J.R. Ellis and D.V. Nanopoulos, An Expanding Universe in String Theory, Nucl. Phys. B 328 (1989) 117 [INSPIRE].
I. Antoniadis, C. Bachas, J.R. Ellis and D.V. Nanopoulos, Comments on cosmological string solutions, Phys. Lett. B 257 (1991) 278 [INSPIRE].
J.G. Russo, Exact solution of scalar tensor cosmology with exponential potentials and transient acceleration, Phys. Lett. B 600 (2004) 185 [hep-th/0403010] [INSPIRE].
E. Dudas, N. Kitazawa and A. Sagnotti, On Climbing Scalars in String Theory, Phys. Lett. B 694 (2011) 80 [arXiv:1009.0874] [INSPIRE].
A. Sagnotti, Brane SUSY breaking and inflation: implications for scalar fields and CMB distortion, arXiv:1303.6685 [INSPIRE].
P. Fré, A. Sagnotti and A.S. Sorin, Integrable Scalar Cosmologies I. Foundations and links with String Theory, Nucl. Phys. B 877 (2013) 1028 [arXiv:1307.1910] [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
D. Kazanas, Dynamics of the Universe and Spontaneous Symmetry Breaking, Astrophys. J. 241 (1980) L59 [INSPIRE].
K. Sato, Cosmological Baryon Number Domain Structure and the First Order Phase Transition of a Vacuum, Phys. Lett. 99B (1981) 66 [INSPIRE].
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
V.F. Mukhanov and G.V. Chibisov, Quantum Fluctuations and a Nonsingular Universe, JETP Lett. 33 (1981) 532 [Pisma Zh. Eksp. Teor. Fiz. 33 (1981) 549] [INSPIRE].
A.D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems, Phys. Lett. 108B (1982) 389 [INSPIRE].
A. Albrecht and P.J. Steinhardt, Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking, Phys. Rev. Lett. 48 (1982) 1220 [INSPIRE].
A.D. Linde, Chaotic Inflation, Phys. Lett. 129B (1983) 177 [INSPIRE].
N. Bartolo, E. Komatsu, S. Matarrese and A. Riotto, Non-Gaussianity from inflation: Theory and observations, Phys. Rept. 402 (2004) 103 [astro-ph/0406398] [INSPIRE].
V. Mukhanov, Physical foundations of cosmology, Cambridge University Press, Cambridge, U.K., (2005).
S. Weinberg, Cosmology, Oxford University Press, Oxford, U.K., (2008).
D.H. Lyth and A.R. Liddle, The primordial density perturbation: Cosmology, inflation and the origin of structure, Cambridge University Press, Cambridge, U.K., (2009).
D.S. Gorbunov and V.A. Rubakov, Introduction to the theory of the early universe: Cosmological perturbations and inflationary theory, World Scientific, Hackensack, U.S.A., (2011).
J. Martin, C. Ringeval and V. Vennin, Encyclopædia Inflationaris, Phys. Dark Univ. 5-6 (2014) 75 [arXiv:1303.3787] [INSPIRE].
E. Dudas, N. Kitazawa, S.P. Patil and A. Sagnotti, CMB Imprints of a Pre-Inflationary Climbing Phase, JCAP 05 (2012) 012 [arXiv:1202.6630] [INSPIRE].
N. Kitazawa and A. Sagnotti, Pre-inflationary clues from String Theory?, JCAP 04 (2014) 017 [arXiv:1402.1418] [INSPIRE].
N. Kitazawa and A. Sagnotti, String theory clues for the low-ℓ CMB?, EPJ Web Conf. 95 (2015) 03031 [arXiv:1411.6396] [INSPIRE].
N. Kitazawa and A. Sagnotti, A string-inspired model for the low-ℓ CMB, Mod. Phys. Lett. A 30 (2015) 1550137 [arXiv:1503.04483] [INSPIRE].
C. Condeescu and E. Dudas, Kasner solutions, climbing scalars and big-bang singularity, JCAP 08 (2013) 013 [arXiv:1306.0911] [INSPIRE].
A. Gruppuso and A. Sagnotti, Observational Hints of a Pre-Inflationary Scale?, Int. J. Mod. Phys. D 24 (2015) 1544008 [arXiv:1506.08093] [INSPIRE].
A. Gruppuso, N. Kitazawa, N. Mandolesi, P. Natoli and A. Sagnotti, Pre-Inflationary Relics in the CMB?, Phys. Dark Univ. 11 (2016) 68 [arXiv:1508.00411] [INSPIRE].
A. Gruppuso, N. Kitazawa, M. Lattanzi, N. Mandolesi, P. Natoli and A. Sagnotti, The Evens and Odds of CMB Anomalies, Phys. Dark Univ. 20 (2018) 49 [arXiv:1712.03288] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, Adv. Theor. Math. Phys. 21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Proof of the Weak Gravity Conjecture from Black Hole Entropy, JHEP 10 (2018) 004 [arXiv:1801.08546] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
S.K. Garg, C. Krishnan and M. Zaid, Bounds on Slow Roll at the Boundary of the Landscape, arXiv:1810.09406 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
O. DeWolfe, D.Z. Freedman, S.S. Gubser, G.T. Horowitz and I. Mitra, Stability of AdS(p) x M(q) compactifications without supersymmetry, Phys. Rev. D 65 (2002) 064033 [hep-th/0105047] [INSPIRE].
S.S. Gubser and I. Mitra, Some interesting violations of the Breitenlohner-Freedman bound, JHEP 07 (2002) 044 [hep-th/0108239] [INSPIRE].
A.M. Polyakov, Quantum Geometry of Bosonic Strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].
A.M. Polyakov, Quantum Geometry of Fermionic Strings, Phys. Lett. B 103 (1981) 211 [INSPIRE].
H. Hochstadt, The Functions of Mathematical Physics, Dover, New York, U.S.A., (1986).
M.A. Rubin and C.R. Ordonez, Eigenvalues and degeneracies for n-dimensional tensor spherical harmonics, UTTG-10-83 (1983), [INSPIRE].
M.A. Rubin and C.R. Ordonez, Symmetric Tensor Eigen Spectrum of the Laplacian on n Spheres, J. Math. Phys. 26 (1985) 65 [INSPIRE].
A. Higuchi, Symmetric Tensor Spherical Harmonics on the N Sphere and Their Application to the de Sitter Group SO(N ,1), J. Math. Phys. 28 (1987) 1553 [Erratum ibid. 43 (2002) 6385] [INSPIRE].
Z.-Q. Ma, Group Theory for Physicists, chapter 9, World Scientific, Singapore, (2007).
E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].
G.T. Horowitz, J. Orgera and J. Polchinski, Nonperturbative Instability of AdS 5 × S 5 /Z(k), Phys. Rev. D 77 (2008) 024004 [arXiv:0709.4262] [INSPIRE].
S.-W. Kim, J. Nishimura and A. Tsuchiya, Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions, Phys. Rev. Lett. 108 (2012) 011601 [arXiv:1108.1540] [INSPIRE].
K.N. Anagnostopoulos, T. Azuma, Y. Ito, J. Nishimura and S.K. Papadoudis, Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models, JHEP 02 (2018) 151 [arXiv:1712.07562] [INSPIRE].
N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115] [INSPIRE].
F. Lucchin and S. Matarrese, Power Law Inflation, Phys. Rev. D 32 (1985) 1316 [INSPIRE].
B. Ratra and P.J.E. Peebles, Cosmological Consequences of a Rolling Homogeneous Scalar Field, Phys. Rev. D 37 (1988) 3406 [INSPIRE].
J.J. Halliwell, Scalar Fields in Cosmology with an Exponential Potential, Phys. Lett. B 185 (1987) 341 [INSPIRE].
L.F. Abbott and M.B. Wise, Constraints on Generalized Inflationary Cosmologies, Nucl. Phys. B 244 (1984) 541 [INSPIRE].
D.H. Lyth and E.D. Stewart, The curvature perturbation in power law (e.g. extended) inflation, Phys. Lett. B 274 (1992) 168 [INSPIRE].
P.G. Ferreira and M. Joyce, Cosmology with a primordial scaling field, Phys. Rev. D 58 (1998) 023503 [astro-ph/9711102] [INSPIRE].
I.P.C. Heard and D. Wands, Cosmology with positive and negative exponential potentials, Class. Quant. Grav. 19 (2002) 5435 [gr-qc/0206085] [INSPIRE].
N. Ohta, Accelerating cosmologies from S-branes, Phys. Rev. Lett. 91 (2003) 061303 [hep-th/0303238] [INSPIRE].
S. Roy, Accelerating cosmologies from M/string theory compactifications, Phys. Lett. B 567 (2003) 322 [hep-th/0304084] [INSPIRE].
P.K. Townsend and M.N.R. Wohlfarth, Accelerating cosmologies from compactification, Phys. Rev. Lett. 91 (2003) 061302 [hep-th/0303097] [INSPIRE].
P.K. Townsend and M.N.R. Wohlfarth, Cosmology as geodesic motion, Class. Quant. Grav. 21 (2004) 5375 [hep-th/0404241] [INSPIRE].
R. Emparan and J. Garriga, A note on accelerating cosmologies from compactifications and S branes, JHEP 05 (2003) 028 [hep-th/0304124] [INSPIRE].
E. Bergshoeff, A. Collinucci, U. Gran, M. Nielsen and D. Roest, Transient quintessence from group manifold reductions or how all roads lead to Rome, Class. Quant. Grav. 21 (2004) 1947 [hep-th/0312102] [INSPIRE].
A.A. Andrianov, F. Cannata and A. Yu. Kamenshchik, General solution of scalar field cosmology with a (piecewise) exponential potential, JCAP 10 (2011) 004 [arXiv:1105.4515] [INSPIRE].
Planck collaboration, Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan and F. Riccioni, IIB supergravity revisited, JHEP 08 (2005) 098 [hep-th/0506013] [INSPIRE].
E.A. Bergshoeff, M. de Roo, S.F. Kerstan, T. Ortín and F. Riccioni, SL(2, ℝ)-invariant IIB Brane Actions, JHEP 02 (2007) 007 [hep-th/0611036] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, String Solitons and T-duality, JHEP 05 (2011) 131 [arXiv:1102.0934] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, Heterotic wrapping rules, JHEP 01 (2013) 005 [arXiv:1210.1422] [INSPIRE].
E.A. Bergshoeff, V.A. Penas, F. Riccioni and S. Risoli, Non-geometric fluxes and mixed-symmetry potentials, JHEP 11 (2015) 020 [arXiv:1508.00780] [INSPIRE].
J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61 [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, 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].
I. Antoniadis and C. Kounnas, Superstring phase transition at high temperature, Phys. Lett. B 261 (1991) 369 [INSPIRE].
E. Kiritsis and C. Kounnas, Perturbative and nonperturbative partial supersymmetry breaking: N = 4 → N = 2 → N = 1, Nucl. Phys. B 503 (1997) 117 [hep-th/9703059] [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 2 freely acting orbifolds, Nucl. Phys. B 565 (2000) 123 [hep-th/9907184] [INSPIRE].
E. Dudas, J. Mourad and A. Sagnotti, Charged and uncharged D-branes in various string theories, Nucl. Phys. B 620 (2002) 109 [hep-th/0107081] [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].
J.D. Blum and K.R. Dienes, From the type-I string to M-theory: A continuous connection, Nucl. Phys. B 520 (1998) 93 [hep-th/9708016] [INSPIRE].
S. Ferrara and A. Sagnotti, Massive Born-Infeld and Other Dual Pairs, JHEP 04 (2015) 032 [arXiv:1502.01650] [INSPIRE].
C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Ya. S. Stanev, Chiral asymmetry in four-dimensional open string vacua, Phys. Lett. B 385 (1996) 96 [hep-th/9606169] [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: 1811.11448
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
Basile, I., Mourad, J. & Sagnotti, A. On classical stability with broken supersymmetry. J. High Energ. Phys. 2019, 174 (2019). https://doi.org/10.1007/JHEP01(2019)174
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)174