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Searching the landscape of flux vacua with genetic algorithms. (English) Zbl 1429.83085
Summary: In this paper, we employ genetic algorithms to explore the landscape of type IIB flux vacua. We show that genetic algorithms can efficiently scan the landscape for viable solutions satisfying various criteria. More specifically, we consider a symmetric \(T^6\) as well as the conifold region of a Calabi-Yau hypersurface. We argue that in both cases genetic algorithms are powerful tools for finding flux vacua with interesting phenomenological properties. We also compare genetic algorithms to algorithms based on different breeding mechanisms as well as random walk approaches.

83E30 String and superstring theories in gravitational theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
68W50 Evolutionary algorithms, genetic algorithms (computational aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
Full Text: DOI arXiv
[1] Bousso, R.; Polchinski, J., Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP, 06, 006 (2000) · Zbl 0990.83543
[2] L. Susskind, The Anthropic landscape of string theory, hep-th/0302219 [INSPIRE]. · Zbl 1188.83105
[3] Douglas, MR, The Statistics of string/M theory vacua, JHEP, 05, 046 (2003)
[4] Banks, T.; Dine, M.; Gorbatov, E., Is there a string theory landscape?, JHEP, 08, 058 (2004)
[5] T. Banks, Landskepticism or why effective potentials don’t count string models, 2004, hep-th/0412129 [INSPIRE].
[6] T. Banks, The Top 10^500Reasons Not to Believe in the Landscape, arXiv:1208.5715 [INSPIRE].
[7] Ashok, S.; Douglas, MR, Counting flux vacua, JHEP, 01, 060 (2004) · Zbl 1243.83060
[8] Denef, F.; Douglas, MR, Distributions of flux vacua, JHEP, 05, 072 (2004)
[9] Douglas, Michael R.; Shiffman, Bernard; Zelditch, Steve, Critical Points and Supersymmetric Vacua I, Communications in Mathematical Physics, 252, 325-358 (2004) · Zbl 1103.32011
[10] Denef, F.; Douglas, MR, Distributions of nonsupersymmetric flux vacua, JHEP, 03, 061 (2005)
[11] L. Susskind, Supersymmetry breaking in the anthropic landscape, hep-th/0405189 [INSPIRE].
[12] M.R. Douglas, Statistical analysis of the supersymmetry breaking scale, hep-th/0405279 [INSPIRE].
[13] Dine, M.; Gorbatov, E.; Thomas, SD, Low energy supersymmetry from the landscape, JHEP, 08, 098 (2008)
[14] Conlon, JP; Quevedo, F., On the explicit construction and statistics of Calabi-Yau flux vacua, JHEP, 10, 039 (2004)
[15] Kallosh, R.; Linde, AD, Landscape, the scale of SUSY breaking and inflation, JHEP, 12, 004 (2004)
[16] Marchesano, Fernando; Shiu, Gary; Wang, Lian-Tao, Model building and phenomenology of flux-induced supersymmetry breaking on D3-branes, Nuclear Physics B, 712, 20-58 (2005) · Zbl 1109.81344
[17] Dine, M.; O’Neil, D.; Sun, Z., Branches of the landscape, JHEP, 07, 014 (2005)
[18] Acharya, BS; Denef, F.; Valandro, R., Statistics of M-theory vacua, JHEP, 06, 056 (2005)
[19] K.R. Dienes, Statistics on the heterotic landscape: Gauge groups and cosmological constants of four-dimensional heterotic strings, Phys. Rev.D 73 (2006) 106010 [hep-th/0602286] [INSPIRE].
[20] F. Gmeiner, R. Blumenhagen, G. Honecker, D. Lüst and T. Weigand, One in a billion: MSSM-like D-brane statistics, JHEP01 (2006) 004 [hep-th/0510170] [INSPIRE].
[21] Douglas, MR; Taylor, W., The Landscape of intersecting brane models, JHEP, 01, 031 (2007)
[22] C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE]. · Zbl 1117.81117
[23] 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]. · Zbl 1117.81117
[24] Palti, E., The Swampland: Introduction and Review, Fortsch. Phys., 67, 1900037 (2019)
[25] Cole, A.; Shiu, G., Topological Data Analysis for the String Landscape, JHEP, 03, 054 (2019) · Zbl 1414.83083
[26] Y.-H. He, Deep-Learning the Landscape, arXiv:1706.02714 [INSPIRE].
[27] D. Krefl and R.-K. Seong, Machine Learning of Calabi-Yau Volumes, Phys. Rev.D 96 (2017) 066014 [arXiv:1706.03346] [INSPIRE].
[28] Ruehle, F., Evolving neural networks with genetic algorithms to study the String Landscape, JHEP, 08, 038 (2017) · Zbl 1381.83128
[29] Carifio, J.; Halverson, J.; Krioukov, D.; Nelson, BD, Machine Learning in the String Landscape, JHEP, 09, 157 (2017) · Zbl 1382.81155
[30] Wang, Y-N; Zhang, Z., Learning non-Higgsable gauge groups in 4D F-theory, JHEP, 08, 009 (2018)
[31] K. Bull, Y.-H. He, V. Jejjala and C. Mishra, Machine Learning CICY Threefolds, Phys. Lett.B 785 (2018) 65 [arXiv:1806.03121] [INSPIRE].
[32] D. Klaewer and L. Schlechter, Machine Learning Line Bundle Cohomologies of Hypersurfaces in Toric Varieties, Phys. Lett.B 789 (2019) 438 [arXiv:1809.02547] [INSPIRE]. · Zbl 1406.14001
[33] Mütter, Andreas; Parr, Erik; Vaudrevange, Patrick K. S., Deep learning in the heterotic orbifold landscape, Nuclear Physics B, 940, 113-129 (2019) · Zbl 1409.81099
[34] Halverson, J.; Nelson, B.; Ruehle, F., Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning, JHEP, 06, 003 (2019) · Zbl 1416.83125
[35] Y.-H. He and S.-J. Lee, Distinguishing Elliptic Fibrations with AI, arXiv:1904.08530 [INSPIRE].
[36] J. Holland, Adaptation in Natural and Artificial Systems, The MIT Press reprinted (1992).
[37] E. David, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, (1989). · Zbl 0721.68056
[38] J. Holland, The Royal Road for Genetic Algorithms: Fitness Landscapes and GA Performance, MIT Press (1992).
[39] C. Reeves and J. Rowe, Genetic Algorithms: Principles and Perspectives, Springer (2002).
[40] R. Haupt, Practical genetic algorithms, Wyley (2004). · Zbl 1072.68089
[41] D. Michalewicz, How to Solve It: Modern Heuristics, Springer (2004). · Zbl 1058.68105
[42] B.C. Allanach, D. Grellscheid and F. Quevedo, Genetic algorithms and experimental discrimination of SUSY models, JHEP07 (2004) 069 [hep-ph/0406277] [INSPIRE].
[43] Akrami, Y.; Scott, P.; Edsjo, J.; Conrad, J.; Bergstrom, L., A Profile Likelihood Analysis of the Constrained MSSM with Genetic Algorithms, JHEP, 04, 057 (2010) · Zbl 1272.81204
[44] S. Abel, D.G. Cerdeño and S. Robles, The Power of Genetic Algorithms: what remains of the pMSSM?, arXiv:1805.03615 [INSPIRE].
[45] T.S. Metcalfe, R.E. Nather and D.E. Winget, Genetic-algorithm-based asteroseismological analysis of the dbv white dwarf gd 358, Astrophys. J.545 (2000) 974 [astro-ph/0008022] [INSPIRE].
[46] M.R. Mokiem, A. de Koter, J. Puls, A. Herrero, F. Najarro and M.R. Villamariz, Spectral analysis of early-type stars using a genetic algorithm based fitting method, Astron. Astrophys.441 (2005) 711 [astro-ph/0506751] [INSPIRE].
[47] V. Rajpaul, Genetic algorithms in astronomy and astrophysics, in Proceedings, 56th Annuall Conference of the South African Institute of Physics (SAIP 2011), Gauteng, South Africa, 12-15 July 2011, pp. 519-524, (2012) [arXiv:1202.1643] [INSPIRE].
[48] S. Nesseris and J. Garćıa-Bellido, A new perspective on Dark Energy modeling via Genetic Algorithms, JCAP11 (2012) 033 [arXiv:1205.0364] [INSPIRE].
[49] Hogan, R.; Fairbairn, M.; Seeburn, N., GAz: A Genetic Algorithm for Photometric Redshift Estimation, Mon. Not. Roy. Astron. Soc., 449, 2040 (2015)
[50] Blåbäck, J.; Danielsson, U.; Dibitetto, G., Fully stable dS vacua from generalised fluxes, JHEP, 08, 054 (2013) · Zbl 1342.83334
[51] Damian, C.; Diaz-Barron, LR; Loaiza-Brito, O.; Sabido, M., Slow-Roll Inflation in Non-geometric Flux Compactification, JHEP, 06, 109 (2013) · Zbl 1342.83352
[52] C. Damian and O. Loaiza-Brito, More stable de Sitter vacua from S-dual nongeometric fluxes, Phys. Rev.D 88 (2013) 046008 [arXiv:1304.0792] [INSPIRE].
[53] Blåbäck, J.; Danielsson, U.; Dibitetto, G., Accelerated Universes from type IIA Compactifications, JCAP, 03, 003 (2014)
[54] J. Blåbäck, D. Roest and I. Zavala, de Sitter Vacua from Nonperturbative Flux Compactifications, Phys. Rev.D 90 (2014) 024065 [arXiv:1312.5328] [INSPIRE].
[55] Abel, S.; Rizos, J., Genetic Algorithms and the Search for Viable String Vacua, JHEP, 08, 010 (2014)
[56] F. Denef and M.R. Douglas, Computational complexity of the landscape. I., Annals Phys.322 (2007) 1096 [hep-th/0602072] [INSPIRE]. · Zbl 1113.83007
[57] N. Bao, R. Bousso, S. Jordan and B. Lackey, Fast optimization algorithms and the cosmological constant, Phys. Rev.D 96 (2017) 103512 [arXiv:1706.08503] [INSPIRE].
[58] Denef, Frederik; Douglas, Michael R.; Greene, Brian; Zukowski, Claire, Computational complexity of the landscape II—Cosmological considerations, Annals of Physics, 392, 93-127 (2018) · Zbl 1390.83337
[59] J. Halverson and F. Ruehle, Computational Complexity of Vacua and Near-Vacua in Field and String Theory, Phys. Rev.D 99 (2019) 046015 [arXiv:1809.08279] [INSPIRE]. · Zbl 1416.83125
[60] Silver, D.; etal., Mastering the game of go with deep neural networks and tree search, Nature, 529, 484 (2016)
[61] T. Salimans, J. Ho, X. Chen, S. Sidor and I. Sutskever, Evolution Strategies as a Scalable Alternative to Reinforcement Learning, arXiv:1703.03864.
[62] Arkani-Hamed, N.; Motl, L.; Nicolis, A.; Vafa, C., The String landscape, black holes and gravity as the weakest force, JHEP, 06, 060 (2007)
[63] Brown, J.; Cottrell, W.; Shiu, G.; Soler, P., Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation, JHEP, 10, 023 (2015) · Zbl 1388.83091
[64] Brown, J.; Cottrell, W.; Shiu, G.; Soler, P., On Axionic Field Ranges, Loopholes and the Weak Gravity Conjecture, JHEP, 04, 017 (2016) · Zbl 1388.83892
[65] Heidenreich, B.; Reece, M.; Rudelius, T., Sharpening the Weak Gravity Conjecture with Dimensional Reduction, JHEP, 02, 140 (2016) · Zbl 1388.83119
[66] Heidenreich, B.; Reece, M.; Rudelius, T., Evidence for a sublattice weak gravity conjecture, JHEP, 08, 025 (2017) · Zbl 1381.83065
[67] Montero, M.; Shiu, G.; Soler, P., The Weak Gravity Conjecture in three dimensions, JHEP, 10, 159 (2016) · Zbl 1390.83123
[68] Andriolo, S.; Junghans, D.; Noumi, T.; Shiu, G., A Tower Weak Gravity Conjecture from Infrared Consistency, Fortsch. Phys., 66, 1800020 (2018)
[69] Charbonneau, P., Genetic Algorithms in Astronomy and Astrophysics, Astrophys. J. Suppl., 101, 309 (1995)
[70] P. Charbonneau and B. Knapp, A user’s guide to pikaia 1.0, Tech. Rep. TN-418+IA, National Center for Atmospheric Research (1995).
[71] P. Charbonneau, An introduction to genetic algorithms for numerical optimization, NCAR Technical Note (2002) 74.
[72] P. Charbonneau, Release notes for pikaia 1.2, Tech. Rep. TN-451+STR, National Center for Atmospheric Research (2002).
[73] T. Jones and S. Forrest, Fitness distance correlation as a measure of problem difficulty for genetic algorithms, in Proc. 6th Int. Conf. on Genetic Algorithms, pp. 184-192 (1995).
[74] P. Collard, A. Gaspar, M. Clergue and C. Escazut, Fitness distance correlation, as statistical measure of genetic algorithm difficulty, revisited, in ECAI, pp. 650-654, Citeseer (1998).
[75] Bryngelson, JD; Onuchic, JN; Socci, ND; Wolynes, PG, Funnels, pathways, and the energy landscape of protein folding: a synthesis, Proteins, 21, 167 (1995)
[76] J. Khoury and O. Parrikar, Search Optimization, Funnel Topography and Dynamical Criticality on the String Landscape, arXiv:1907.07693 [INSPIRE].
[77] Ruml, W.; Ngo, JT; Marks, J.; Shieber, SM, Easily searched encodings for number partitioning, J. Optim. Theory. Appl., 89, 251 (1996) · Zbl 0853.90096
[78] Graña, M., Flux compactifications in string theory: A Comprehensive review, Phys. Rept., 423, 91 (2006)
[79] Douglas, MR; Kachru, S., Flux compactification, Rev. Mod. Phys., 79, 733 (2007) · Zbl 1205.81011
[80] S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev.D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
[81] DeWolfe, O.; Giryavets, A.; Kachru, S.; Taylor, W., Enumerating flux vacua with enhanced symmetries, JHEP, 02, 037 (2005)
[82] S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys.B 584 (2000) 69 [Erratum ibid.B 608 (2001) 477] [hep-th/9906070] [INSPIRE]. · Zbl 0984.81143
[83] J.E. Baker, Reducing bias and inefficiency in the selection algorithm, in Proceedings of the second international conference on genetic algorithms, vol. 206, pp. 14-21 (1987).
[84] D.E. Goldberg, Genetic algorithms in search, Optimization, and MachineLearning, Addison-Wesley Longman Publishing Co., Inc. (1989).
[85] L.D. Whitley et al., The genitor algorithm and selection pressure: why rank-based allocation of reproductive trials is best, in Icga, vol. 89, pp. 116-123, Fairfax, VA (1989).
[86] Saliby, E., Descriptive sampling: a better approach to monte carlo simulation, J. Oper. Res. Soc., 41, 1133 (1990)
[87] D.E. Goldberg and K. Deb, A comparative analysis of selection schemes used in genetic algorithms, in Foundations of genetic algorithms, vol. 1, pp. 69-93, Elsevier (1991).
[88] H. Mühlenbein and D. Schlierkamp-Voosen, The science of breeding and its application to the breeder genetic algorithm, Evol. Comput.1 (1994) 335.
[89] P.J. Hancock, An empirical comparison of selection methods in evolutionary algorithms, in AISB Workshop on Evolutionary Computing, pp. 80-94, Springer (1994).
[90] Hancock, PJ, Selection methods for evolutionary algorithms, Practical Handbook of Genetic Algorithms, 2, 67 (1995)
[91] Blickle, T.; Thiele, L., A comparison of selection schemes used in evolutionary algorithms, Evol. Comput., 4, 361 (1996)
[92] D. Thierens, Selection schemes, elitist recombination, and selection intensity, vol. 1998, Utrecht University: Information and Computing Sciences (1998).
[93] S.L. Lohr, Sampling: Design and analysis, CRC Press(1999). · Zbl 0967.62005
[94] G. Rudolph, Takeover times and probabilities of non-generational selection rules, in Proceedings of the 2nd Annual Conference on Genetic and Evolutionary Computation, pp. 903-910, Morgan Kaufmann Publishers Inc. (2000).
[95] G. Rudolph, Takeover times of noisy non-generational selection rules that undo extinction, in Artificial Neural Nets and Genetic Algorithms, pp. 268-271, Springer (2001). · Zbl 1011.68169
[96] C. Reeves and J. Rowe, Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory, vol. 20, Springer Science & Business Media (2002). · Zbl 1029.90081
[97] R.L. Haupt and S. Ellen Haupt, Practical genetic algorithms, John Wiley & Sons, Inc. (2004). · Zbl 1072.68089
[98] Betzler, P.; Plauschinn, E., Type IIB flux vacua and tadpole cancellation, Fortsch. Phys., 67, 1900065 (2019)
[99] Giryavets, A.; Kachru, S.; Tripathy, PK; Trivedi, SP, Flux compactifications on Calabi-Yau threefolds, JHEP, 04, 003 (2004)
[100] Giryavets, A.; Kachru, S.; Tripathy, PK, On the taxonomy of flux vacua, JHEP, 08, 002 (2004)
[101] S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev.D 68 (2003) 046005 [hep-th/0301240] [INSPIRE]. · Zbl 1244.83036
[102] V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP03 (2005) 007 [hep-th/0502058] [INSPIRE].
[103] A. Westphal, de Sitter string vacua from Kähler uplifting, JHEP03 (2007) 102 [hep-th/0611332] [INSPIRE].
[104] Cirafici, M., Persistent Homology and String Vacua, JHEP, 03, 045 (2016) · Zbl 1388.81505
[105] H. Edelsbrunner, D. Letscher and A. Zomorodian, Topological persistence and simplification, in Proceedings 41st Annual Symposium on Foundations of Computer Science, pp. 454-463, IEEE (2000). · Zbl 1011.68152
[106] A. Zomorodian and G. Carlsson, Computing persistent homology, Discrete Comput. Geom.33 (2005) 249. · Zbl 1069.55003
[107] Carlsson, G., Topology and data, Bull. Am. Math. Soc., 46, 255 (2009) · Zbl 1172.62002
[108] Carlsson, G., Topological pattern recognition for point cloud data, Acta Numer., 23, 289 (2014) · Zbl 1398.68615
[109] Cole, A.; Shiu, G., Persistent Homology and Non-Gaussianity, JCAP, 03, 025 (2018)
[110] J. Murugan and D. Robertson, An Introduction to Topological Data Analysis for Physicists: From LGM to FRBs, arXiv:1904.11044 [INSPIRE].
[111] Metropolis, N.; Rosenbluth, AW; Rosenbluth, MN; Teller, AH; Teller, E., Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087 (1953)
[112] Kirkpatrick, S.; Gelatt, C.; Vecchi, M., Simulated annealing methods, J. Stat. Phys, 34, 975 (1984) · Zbl 1225.90162
[113] Kachru, S.; Schulz, MB; Trivedi, S., Moduli stabilization from fluxes in a simple IIB orientifold, JHEP, 10, 007 (2003)
[114] G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
[115] Ooguri, Hirosi; Palti, Eran; Shiu, Gary; Vafa, Cumrun, Distance and de Sitter conjectures on the Swampland, Physics Letters B, 788, 180-184 (2019)
[116] Denef, F.; Douglas, MR; Florea, B., Building a better racetrack, JHEP, 06, 034 (2004)
[117] Conlon, JP; Quevedo, F.; Suruliz, K., Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP, 08, 007 (2005)
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