DISCRETE QUANTUM FIELD THEORIES AND THE INTERSECTION FORM

Abstract

It is shown that the standard mod-p valued intersection form can be used to define Boltzmann weights of subdivision invariant lattice models with gauge group Zp. In particular, we discuss a four-dimensional model which is based on the assignment of field variables to the two-simplices of the simplicial complex. The action is taken to be the intersection form defined on the second cohomology group of the complex, with coefficients in Zp. Subdivision invariance of the theory follows when the coupling constant is quantized and the field configurations are restricted to those satisfying a mod-p flatness condition. We present an explicit computation of the partition function for the manifold ± CP 2, demonstrating non-triviality.