Principal Investigator: David R. Morrison, Paul S. Aspinwall, M. Ronen Plesser
A D-brane, roughly, is something on which an open string may end. Any detailed exploration of this notion quickly reveals that the rough notion is too crude, and that all of the subtleties of the geometry of string theory come into play in full force in describing D-branes. The proposers will investigate both the mathematical and physical properties of D-branes, drawing upon techniques from algebraic geometry (particularly complex threefolds), homological algebra, and derived categories on the mathematics side, and on quantum field theory and supergravity from the physics side. The proposers anticipate that the study of the complementary mathematical and physical aspects of this story will shed light on each other, and that new results in both pure mathematics and theoretical physics will be obtained as a consequence.
This study is part of a broader exploration of the mathematical aspects of an important current theme in theoretical physics: modeling the particles and forces of nature using one-dimensional objects ("strings") instead of the traditional zero-dimensional objects ("points"). Physical models of this kind are quantum-mechanical in nature but also model the gravitational force, thus reconciling one of the great puzzles in theoretical physics (namely, the apparent incompatibility of quantum mechanics and Einstein's theory of gravity). One of the important discoveries of the past decade is that strings may have endpoints which are constrained to lie in particular directions. The places where the endpoints of strings "attach" are known as D-branes, and these will be the subject of detailed mathematical study in the current project.
