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Register a new userTowards machine learning in the classification of Z2xZ2 orbifold compactifications
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Systematic classification of Z2xZ2 orbifold compactifications of the heterotic-string was pursued by using its free fermion formulation. The method entails random generation of string vacua and analysis of their entire spectra, and led to discovery of spinor-vector duality and three generation exophobic string vacua. The classification was performed for string vacua with unbroken SO(10) GUT symmetry, and progressively extended to models in which the SO(10) symmetry is broken to the SO(6)xSO(4), SU(5)xU(1), SU(3)xSU(2)xU(1)^2 and SU(3)xU(1)xSU(2)^2 subgroups. Obtaining sizeable number of phenomenologically viable vacua in the last two cases requires identification of fertility conditions. Adaptation of machine learning tools to identify the fertility conditions will be useful when the frequency of viable models becomes exceedingly small in the total space of vacua.
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We thoroughly analyze the number of independent zero modes and their zero points on the toroidal orbifold $T^2/mathbb{Z}_N$ ($N = 2, 3, 4, 6$) with magnetic flux background, inspired by the Atiyah-Singer index theorem. We first show a complete list for the number $n_{eta}$ of orbifold zero modes belonging to $mathbb{Z}_{N}$ eigenvalue $eta$. Since it turns out that $n_{eta}$ quite complicatedly depends on the flux quanta $M$, the Scherk-Schwarz twist phase $(alpha_1, alpha_2)$, and the $mathbb{Z}_{N}$ eigenvalue $eta$, it seems hard that $n_{eta}$ can be universally explained in a simple formula. We, however, succeed in finding a single zero-mode counting formula $n_{eta} = (M-V_{eta})/N + 1$, where $V_{eta}$ denotes the sum of winding numbers at the fixed points on the orbifold $T^2/mathbb{Z}_N$. The formula is shown to hold for any pattern.
We study (4+2n)-dimensional N=1 super Yang-Mills theory on the orbifold background with non-vanishing magnetic flux. In particular, we study zero-modes of spinor fields. The flavor structure of our models is different from one in magnetized torus models, and would be interesting in realistic model building.
We consider 4d string compactifications in the presence of fluxes, and classify particles, strings and domain walls arising from wrapped branes which have charges conserved modulo an integer p, and whose annihilation is catalized by fluxes, through the Freed-Witten anomaly or its du
The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which both Synthetic Minority Oversampling Technique (SMOTE) and permutations of the CICY matrix are used to decrease the class imbalance and improve performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned.
We extend the KKLT approach to moduli stabilization by including the dilaton and the complex structure moduli into the effective supergravity theory. Decoupling of the dilaton is neither always possible nor necessary for the existence of stable minima with zero (or positive) cosmological constant. The pattern of supersymmetry breaking can be much richer than in the decoupling scenario of KKLT.
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