• Critical Dimension
• Renormalization
• General Relativity
• Conformal Field Theories
• Brane
• String Theory

String theory is one of the most ambitious and fascinating projects in the history of
theoretical physics. It purports to be an all-encompassing theory of the universe, unifying the forces of Nature, including gravity, in a single quantum mechanical framework. Using the only assumption that all particles are, at a fundamental level, excitations of one-dimensional strings, the theory tries to create a model in which general relativity, electromagnetism and Yang-Mills gauge theories emerge.
A particularly successful feature of the string theory framework is to consistently reproduce the dynamics of spacetime in the form of Einstein’s equations. In fact, they emerge at low energies, through the requirment of internal consistency of string theory, if seen as a field theory. Together with Einstein’s equations, string theory also predicts the number of spacetime dimensions, known as critical dimension, which is a rather unique achievement if compared to other approaches. In fact, the string is believed to be the unique theory which is capable of such goals.
In this thesis, we introduce an entirely new four dimensional object that we call the 4-brane and we show, following the ideas of string theory, that it can play the very active role of producing Einstein’s equations at low energies. Even though these conclusions must be taken with a grain of salt, especially because much more work is needed to truly establish the 4-brane as a completely consistent object, we could speculate that the new four dimensional object is a serious contender to the uniqueness of the string.