Speaker: Derek K. Wise
Title: Discrete p-form Electromagnetism as a Chain Field Theory
Abstract: Since Wilson's work on lattice gauge theory (LGT) in the 1970s, discrete versions of field theories have played an important role in fundamental physics, including loop quantum gravity. More recent work makes it natural to generalize LGT in two directions. First, the usual formulation of LGT approximates Euclidean spacetime by a graph whose vertices form a regular cubical lattice. Although this proves a powerful computational tool for understanding continuum gauge theory, the quantum geometer's interest in manifestly discrete spacetimes makes it desirable to generalize LGT to accommodate `lattices' of a much more general sort. Second, there is recent interest in higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian generalizations. It is natural to discretize such `higher gauge theories' in a way analogous to lattice gauge theory, but with the fundamental geometric structures in the discretization boosted in dimension. As a step toward studying discrete versions of more general higher gauge theories, we consider the case of p-form electromagnetism. We show that discrete p-form electromagnetism can be described as a `chain field theory' --- a theory analogous to topological quantum field theory, but with chain complexes replacing manifolds.
Talk: Transparencies, Recorded Talk