Computational methods in string and field theory
Pontiggia, Luca Terzio
Like any field or topic of research, significant advancements can be made with increasing computational power - string theory is no exception. In this thesis, an analysis is performed within three areas: Calabi–Yau manifolds, cosmological inflation and application of conformal field theory. Critical superstring theory is a ten dimensional theory. Four of the dimensions refer to the spacetime dimensions we see in nature. To account for the remaining six, Calabi-Yau manifolds are used. Knowing how the space of Calabi-Yau manifolds is distributed gives valuable insight into the compactification process. Using computational modeling and statistical analysis, previously unseen patterns of the distribution of the Hodge numbers are found. In particular, patterns in frequencies exhibit striking new patterns - pseudo-Voigt and Planckian distributions with high confidence and exact fits for many substructures. The patterns indicate typicality within the landscape of Calabi–Yau manifolds of various dimensions. Inflation describes the exponential expansion of the universe after the Big Bang. Finding a successful theory of inflation centres around building a potential of the inflationary field, such that it satisfies the slow-roll conditions. The numerous ways this can be done, coupled with the fact that each model is highly sensitive to initial conditions, means an analytic approach is often not feasible. To bypass this, a statistical analysis of a landscape of thousands of random single and multifield polynomial potentials is performed. Investigation of the single field case illustrates a window in which the potentials satisfy the slow-roll conditions. When there are two scalar fields, it is found that the probability depends on the choice of distribution for the coefficients. A uniform distribution yields a 0.05% probability of finding a suitable minimum in the random potential whereas a maximum entropy distribution yields a 0.1% probability. The benefit of developing computational tools extends into the interdisciplinary study between conformal field theory and the theory of how wildfires propagate. Using the two dimensional Ising model as a basis of inspiration, computational methods of analyzing how fires propagate provide a new tool set which aids in the process of both modeling large scale wildfires as well as describing the emergent scale invariant structure of these fires. By computing the two point and three point correlations of fire occurrences in particular regions within Botswana and Kazakhstan, it is shown that this proposed model gives excellent fits, with the model amplitude being directly proportional to the total burn area of a particular year.
Thesis is submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the University of the Witwatersrand, Faculty of Science, School of Physics, University of the Witwatersrand, Johannesburg, 2018
Pontiggia, Luca Terzio (2018) Computational methods in string and field theory, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/25803>