The infrared /ultraviolet connection in string theory

In conventional (20th century) physics, high energy or high momentum came to be associated with short distances. The physics of the 21st century is likely to be dominated by a very different perspective. According to the infrared/ultraviolet connection which underlies much of our new understanding of string theory and its connection to gravity, physics of increasing energy or momentum is governed by increasingly large distances. In this thesis, we investigate thoroughly several such examples of infrared/ultraviolet mixing that occur in string theory and analyze their consequences and implications for gravity. Examples include the growth of particle size with momentum, giant gravitons, the infrared/ultraviolet connection in the holographic description of AdS spaces, space/time non commutativity in the context of open string theories and the spacetime uncertainty principle of string theory DxDt∼l2s . We also study the consequences of similar uncertainty principles that occur in non-commutative geometry where the coordinates of space do not commute. An important consequence of the non-commutativity is the fact that the particles described by non-commutative field theories have a spatial extension which is proportional to their momentum. This in turn leads to unfamiliar violations of the conventional decoupling of infrared and ultraviolet degrees of freedom in these theories. A final chapter is concerned with the description of large brane configurations in type IIA string theory whose low energy dynamics is described by the Quantum Hall effect. An interesting interplay of infrared/ultraviolet mixing phenomena occurs in the description.