Lichtenberg Endowed Professorship: The Fundamental Structure of String Theory and Its Relation to Gauge Field Theories

The general area of research of the proposed Lichtenberg professorship is in string theory and quantum field theory, a very active branch of modern mathematical physics, with strong ties to elementary particle physics, gravitation and mathematics. String theory is the most promising candidate for a unification of gravity with the other three fundamental forces of nature in a quantum mechanically consistent framework. It is built upon the simple and elegant proposal of replacing the concept of a point-like elementary particle by an extended one-dimensional string-like object which vibrates. The various vibration modes of the string correspond to the spectrum of elementary particles observed in nature. The graviton as the quantum carrier of the gravitational force is part of the string vibration spectrum, thus surpassing a deficiency of quantum theories built upon point-particles which fail to describe the graviton. Our present understanding of string theory is still incomplete and the model has not been experimentally verified. Nevertheless, it predicts the existence of a symmetry between bosonic and fermionic particles ( supersymmetry ) which would be of great relevance in particle physics and will be searched for in the next generation of accelerators. Moreover, strings predict the existence of six additional compact dimensions in our universe. One focus of the professorship will be to deepen the understanding of the fundamental structure of string theory through its relation to supermembranes and matrix theories. The non-perturbative structure of string theory has only recently been better understood, through a unification of all five ten-dimensional string theories into a more complete underlying framework, known as M-theory. Its fundamental degrees of freedom might be provided by membranes. In this framework, matrix theories appear as discretized descriptions of membranes. The second focus of the proposal is directed toward the study of dualities of strings and gauge theories. Gauge theories are the essential building blocks of the Standard Model of Elementary Particle Physics, but their strong coupling dynamics to date is not accessible by analytic means. In recent years strings have emerged as a novel tool to study strongly coupled gauge theories through a dual string formulation. In this setting integrable structures related to spin chain models have appeared, which might hold the key to a complete solution for the (large N) spectra of gauge theories.