P-CELL GAUGE THEORIES, MANIFOLD SPACE, AND MULTI-DIMENSIONAL INTEGRABILITY

We construct lattice gauge theories where the gauge potentials live on p-cells, using ideas from the theory of multi-dimensional lattice integrability. The classical limit of these models can naturally be considered as chiral models in the space ΩPM of p-dimensional manifolds on M, or alternatively as gauge theories in ΩP−1M. The continuum models have an infinite set of functionally conserved currents in ΩPM, which are classical analogs of the simplex equations of lattice integrable systems.