Z2 Lattice Gerbe Theory
Abstract
2-form abelian and non-abelian gauge fields on d-dimensional hypercubic lattices have been discussed in the past by various authors and most recently by Lipstein and Reid-Edwards. In this note we recall that the Hamiltonian of a Z2 variant of such theories is one of the family of generalized Ising models originally considered by Wegner. For such "Z2 lattice gerbe theories" general arguments can be used to show that a phase transition for Wilson surfaces will occur for d>3 between volume and area scaling behaviour. In 3d the model is equivalent under duality to an infinite coupling model and no transition is seen, whereas in 4d the model is dual to the 4d Ising model and displays a continuous transition. In 5d the Z2 lattice gerbe theory is self-dual in the presence of an external field and in 6d it is self-dual in zero external field.