119 research outputs found

    From Veneziano to Riemann: A string theory statement of the Riemann hypothesis

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    We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis formulated in terms of integrals of the logarithm and the argument of the zeta function. We also discuss how the integral criterion based on the argument of the Riemann zeta function relates to the Li criterion for the Riemann hypothesis. We provide a new generalization of this integral criterion. Finally, we comment on the physical interpretation of our recasting of the Riemann hypothesis in terms of the Veneziano amplitude

    Getting CICY high

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    Supervised machine learning can be used to predict properties of string geometries with previously unknown features. Using the complete intersection Calabi–Yau (CICY) threefold dataset as a theoretical laboratory for this investigation, we use low h1,1 geometries for training and validate on geometries with large h1,1. Neural networks and Support Vector Machines successfully predict trends in the number of Kähler parameters of CICY threefolds. The numerical accuracy of machine learning improves upon seeding the training set with a small number of samples at higher h1,1

    Machine learning CICY threefolds

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    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

    The Library of Babel

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    We show that heavy pure states of gravity can appear to be mixed states to almost all probes. Our arguments are made for AdS5\rm{AdS}_5 Schwarzschild black holes using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory operators capable of describing very heavy states in gravity. For certain supersymmetric states of the theory, our account is exact: the microstates are described in gravity by a spacetime ``foam'', the precise details of which are invisible to almost all probes.Comment: 7 pages, 1 figure, Essay receiving honorable mention in the 2005 Gravity Research Foundation essay competitio

    Nonsupersymmetric smooth geometries and D1-D5-P bound states

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    We construct smooth nonsupersymmetric soliton solutions with D1-brane, D5-brane, and momentum charges in type IIB supergravity compactified on T4×S1, with the charges along the compact directions. This generalizes previous studies of smooth supersymmetric solutions. The solutions are obtained by considering a known family of U(1)×U(1) invariant metrics, and studying the conditions imposed by requiring smoothness. We discuss the relation of our solutions to states in the CFT describing the D1-D5 system and describe various interesting features of the geometry

    Infinite statistics, symmetry breaking and combinatorial hierarchy

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    The physics of symmetry breaking in theories with strongly interacting quanta obeying infinite (quantum Boltzmann) statistics known as quons is discussed. The picture of Bose/Fermi particles as low energy excitations over nontrivial quon condensate is advocated. Using induced gravity arguments it is demonstrated that the Planck mass in such low energy effective theory can be factorially (in number of degrees of freedom) larger than its true ultraviolet cutoff. Thus, the assumption that statistics of relevant high energy excitations is neither Bose nor Fermi but infinite can remove the hierarchy problem without necessity to introduce any artificially large numbers. Quantum mechanical model illustrating this scenario is presented.Comment: LaTeX, 11 page