Geometry of gerbes & D-branes

This project would lay down some of mathematical ground for string theory.

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This project is open for Honours, Masters and PhD students.
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About

In the mathematical theory of electromagnetic fields, we know that the phases of moving a point particle around a closed path can in part be described in terms of a bundle with connection, a system of locally defined 1-forms glued together via the valued transition functions associated to the underlying bundle.

In string theory, a particle is described as a tiny /openclosed string the phases of moving a string around can be described in terms of a gerbe with connection and a curving. This curving is a system of locally defined 2-forms called the Kalb-Ramond field. The phase is sometimes called the holonomy along a closed surface (a closed trajectory of a string particle).

Strings can have various kinds of boundary conditions. Open strings can have different kinds of boundary conditions called Neumann and Dirichlet boundary conditions such that the endpoint of a string is fixed to move only on some submanifold, called the support of the D-brane. D-branes are actually dynamical objects which have fluctuations and can move around. All these require some deep understanding of geometry of gerbes. D-branes have found many interesting applications in theoretical physics and mathematics.

This project would lay down some of mathematical ground for string theory.

Members

Supervisor

Bryan Wang

Associate Professor
HDR Convenor