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Machine learning in the string landscape. (English) Zbl 1382.81155
Summary: We utilize machine learning to study the string landscape. Deep data dives and conjecture generation are proposed as useful frameworks for utilizing machine learning in the landscape, and examples of each are presented. A decision tree accurately predicts the number of weak Fano toric threefolds arising from reflexive polytopes, each of which determines a smooth F-theory compactification, and linear regression generates a previously proven conjecture for the gauge group rank in an ensemble of $$\frac{4}{3}\times 2.96\times {10}^{755}$$ F-theory compactifications. Logistic regression generates a new conjecture for when $$E_6$$ arises in the large ensemble of F-theory compactifications, which is then rigorously proven. This result may be relevant for the appearance of visible sectors in the ensemble. Through conjecture generation, machine learning is useful not only for numerics, but also for rigorous results.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 83E30 String and superstring theories in gravitational theory 68T05 Learning and adaptive systems in artificial intelligence 62P35 Applications of statistics to physics 62J12 Generalized linear models (logistic models)
##### Keywords:
D-branes; F-theory; superstring vacua
py-junctions
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##### References:
 [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] Ashok, S.; Douglas, MR, Counting flux vacua, JHEP, 01, 060, (2004) · Zbl 1243.83060 [3] Denef, F.; Douglas, MR, Distributions of flux vacua, JHEP, 05, 072, (2004) [4] Taylor, W.; Wang, Y-N, The F-theory geometry with most flux vacua, JHEP, 12, 164, (2015) · Zbl 1388.81367 [5] J. Halverson, C. Long and B. Sung, On Algorithmic Universality in F-theory Compactifications, arXiv:1706.02299 [INSPIRE]. · Zbl 1388.81013 [6] F. Denef and M.R. Douglas, Computational complexity of the landscape. I., Annals Phys.322 (2007) 1096 [hep-th/0602072] [INSPIRE]. · Zbl 1388.81871 [7] Cvetič, M.; Garcia-Etxebarria, I.; Halverson, J., On the computation of non-perturbative effective potentials in the string theory landscape: IIB/F-theory perspective, Fortsch. Phys., 59, 243, (2011) · Zbl 1209.81162 [8] F. Denef, M.R. Douglas, B. Greene and C. Zukowski, Computational complexity of the landscape II — Cosmological considerations, arXiv:1706.06430 [INSPIRE]. · Zbl 1390.83337 [9] N. Bao, R. Bousso, S. Jordan and B. Lackey, Fast optimization algorithms and the cosmological constant, arXiv:1706.08503 [INSPIRE]. · Zbl 1361.81117 [10] Y.-H. He, Deep-Learning the Landscape, arXiv:1706.02714 [INSPIRE]. · Zbl 1397.14048 [11] Ruehle, F., Evolving neural networks with genetic algorithms to study the string landscape, JHEP, 08, 038, (2017) · Zbl 1381.83128 [12] D. Krefl and R.-K. Seong, Machine Learning of Calabi-Yau Volumes, arXiv:1706.03346 [INSPIRE]. · Zbl 1388.81722 [13] T. Mitchell, Machine Learning, McGraw-Hill (1997). · Zbl 0913.68167 [14] C. Bishop, Pattern Recognition and Machine Learning, Springer Publishing Company (2006). · Zbl 1107.68072 [15] Kreuzer, M.; Skarke, H., Classification of reflexive polyhedra in three-dimensions, Adv. Theor. Math. Phys., 2, 847, (1998) · Zbl 0934.52006 [16] Halverson, J.; Tian, J., Cost of seven-brane gauge symmetry in a quadrillion F-theory compactifications, Phys. Rev., D 95, (2017) [17] Vafa, C., Evidence for F-theory, Nucl. Phys., B 469, 403, (1996) · Zbl 1003.81531 [18] D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2., Nucl. Phys.B 476 (1996) 437 [hep-th/9603161] [INSPIRE]. · Zbl 0925.14005 [19] N. Nakayama, On Weierstrass models, in Algebraic geometry and commutative algebra. Volume II, Kinokuniya, Tokyo Japan (1988), pp. 405-431. [20] Anderson, LB; Taylor, W., Geometric constraints in dual F-theory and heterotic string compactifications, JHEP, 08, 025, (2014) [21] Marsano, J.; Schäfer-Nameki, S., Yukawas, G-flux and spectral covers from resolved Calabi-yau’s, JHEP, 11, 098, (2011) · Zbl 1306.81258 [22] Lawrie, C.; Schäfer-Nameki, S., The Tate form on steroids: resolution and higher codimension fibers, JHEP, 04, 061, (2013) · Zbl 1342.81302 [23] Hayashi, H.; Lawrie, C.; Morrison, DR; Schäfer-Nameki, S., Box graphs and singular fibers, JHEP, 05, 048, (2014) · Zbl 1333.81369 [24] Braun, AP; Schäfer-Nameki, S., Box graphs and resolutions I, Nucl. Phys., B 905, 447, (2016) · Zbl 1332.81127 [25] Braun, AP; Schäfer-Nameki, S., Box graphs and resolutions II: from Coulomb phases to fiber faces, Nucl. Phys., B 905, 480, (2016) · Zbl 1332.81128 [26] Grassi, A.; Halverson, J.; Shaneson, JL, Matter from geometry without resolution, JHEP, 10, 205, (2013) · Zbl 1342.83216 [27] Grassi, A.; Halverson, J.; Shaneson, JL, Non-abelian gauge symmetry and the Higgs mechanism in F-theory, Commun. Math. Phys., 336, 1231, (2015) · Zbl 1311.81197 [28] A. Grassi, J. Halverson and J.L. Shaneson, Geometry and Topology of String Junctions, arXiv:1410.6817 [INSPIRE]. · Zbl 1346.81110 [29] A. Grassi, J. Halverson, F. Ruehle and J.L. Shaneson, Dualities of Deformed$$\mathcal{N}=2$$SCFTs from Link Monodromy on D3-brane States, arXiv:1611.01154 [INSPIRE]. · Zbl 1382.81180 [30] Morrison, DR; Taylor, W., Classifying bases for 6D F-theory models, Central Eur. J. Phys., 10, 1072, (2012) · Zbl 1255.81210 [31] Grassi, A.; Halverson, J.; Shaneson, J.; Taylor, W., Non-higgsable QCD and the standard model spectrum in F-theory, JHEP, 01, 086, (2015) · Zbl 1388.81924 [32] Braun, AP; Watari, T., The vertical, the horizontal and the rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications, JHEP, 01, 047, (2015) · Zbl 1388.81495 [33] Watari, T., Statistics of F-theory flux vacua for particle physics, JHEP, 11, 065, (2015) [34] Halverson, J., Strong coupling in F-theory and geometrically non-higgsable seven-branes, Nucl. Phys., B 919, 267, (2017) · Zbl 1361.81117 [35] Halverson, J.; Taylor, W., $${\text{\mathbb{P}}}^1$$-bundle bases and the prevalence of non-higgsable structure in 4D F-theory models, JHEP, 09, 086, (2015) · Zbl 1388.81722 [36] Taylor, W.; Wang, Y-N, A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua, JHEP, 01, 137, (2016) · Zbl 1388.81013 [37] Morrison, DR; Taylor, W., Non-higgsable clusters for 4D F-theory models, JHEP, 05, 080, (2015) · Zbl 1388.81871 [38] Morrison, DR; Taylor, W., Toric bases for 6D F-theory models, Fortsch. Phys., 60, 1187, (2012) · Zbl 1255.81210 [39] Taylor, W., On the Hodge structure of elliptically fibered Calabi-Yau threefolds, JHEP, 08, 032, (2012) · Zbl 1397.14048 [40] D.R. Morrison and W. Taylor, Sections, multisections and U(1) fields in F-theory, arXiv:1404.1527 [INSPIRE]. · Zbl 1348.83091 [41] Martini, G.; Taylor, W., 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces, JHEP, 06, 061, (2015) · Zbl 1388.83862 [42] Johnson, SB; Taylor, W., Calabi-Yau threefolds with large h\^{2,1}, JHEP, 10, 23, (2014) · Zbl 1333.81384 [43] W. Taylor and Y.-N. Wang, Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua, arXiv:1504.07689 [INSPIRE]. · Zbl 1386.14150 [44] J.A. De Loera, J. Rambau and F. Santos, Triangulations: Structures for Algorithms and Applications, 1st edition, Springer Publishing Company (2010). · Zbl 1207.52002
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