Research • Research Areas

Mathematical Physics

String theory is generally considered to be the most promising candidate for the quantum theory of gravity and the Theory of Everything (TOE). Superstrings contain bosons (such as photons and gravitons) as well as fermions (such as electrons) with strictly specified interactions. From a mathematical point of view, bosonic string states and vertex operators offer the most direct representation of the Monster, the biggest simple finite group. The structure constants of the Fake Monster Lie algebra can be shown to be identical with 3-string amplitudes, suggesting that the natural symmetry of String Field theory may be based on the Monster. Other sporadic finite groups and hyperbolic Lie algebras are worthy of study due to the insights they may provide into string theory. Furthermore, string theory can still be useful in hadron phenomenology, where it originated.

Although string theories require 10 or 11 or 26 dimensional space-times, our perceived universe is four dimensional. This may be a consequence of some very special properties of 4-manifolds. For example, there are uncountably many distinct R4's. 4-manifolds are also unique in harboring selfdual gauge fields and Weyl spinors when the metric has Euclidean signature.

Faculty: Cihan Saclioglu