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 $Z_p$. In particular, we discuss a four dimensional model which is based upon the assignment of field variables to the $2$-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 $Z_p$. 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 $\pm C{P}^2$, demonstrating non-triviality.

10 pages, Latex, ITFA-94-19

References in corpus (1)

• State Sum Models and Simplicial Cohomology

Cited by in corpus (3)

• A geometric discretisation scheme applied to the Abelian Chern-Simons theory
• State Sum Models and Simplicial Cohomology
• Topological Modes in Dual Lattice Models