Superstring world-sheet on the lattice

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String theory is a model of theoretical physics for which the fundamental entities in nature are not point-like, but one-dimensional string-like objects - the strings. This model has primarily attracted the attention of physicists and mathematicians as a possible way to unify the description of the fundamental forces in nature, but it has never been proven by experiments. Despite this, it is a primary area of research in theoretical physics in its role of powerful trigger for novel structures in mathematics and new ideas in particle physics. In particular, twenty years ago string theory has been indicated as a tool to understand some universal features of gauge theories, which represent the current, standard way to describe the world around us and its interactions (e.g. the theory of electromagnetism is a gauge theory). This breakthrough idea, known as gauge/string duality, is the conjecture that if strings move through a certain curved spacetime then their dynamics is dual to (has the same behavior of) the dynamics of a certain physical quantity in a specific gauge theory. Now, the study of any gauge theory quantity becomes hard or impossible in the regime in which a certain parameter describing the strength of the interaction - the coupling - is big. Crucially, such so-called strong coupling regime of the gauge theory coincides according to the gauge/string duality with the one in which the study of string theory is straightforward, and vice versa. Therefore, if the duality is true, using string theory one can have easy access to physical information that cannot be obtained in other obvious ways. What is more, recent progress has suggested that some specific gauge theories (and their string dual) may be exactly integrable, namely it may be possible to predict the behavior of some characteristic physical observables at all values of the coupling! If true, one of the dreams of every theoretical particle physicist comes true: having a single formula for the "quark-antiquark" potential (albeit in a very specific gauge theory) as a function of the coupling is now possible!To verify these conjectures (the integrability of the models, the gauge/string duality itself) as well as to try extending the all-coupling analysis to general, non-integrable examples, one should perform a study of either one of the models in a way that is potentially able to explore its strong coupling regime with no assumptions needed. A known way to proceed is to discretize the spacetime in which the model is defined onto a lattice. From being a system with an infinite number of degrees of freedom (related to its original nature in the continuum), the model becomes a statistical system with Nd degrees of freedom (where N is the length of the lattice in one dimension, d is the number of spacetime dimensions) which may then be studied with numerical algorithms known as Monte Carlo methods. This project is about the use of Monte Carlo methods for string theory models relevant in the gauge/string duality.