Discrete Quantum Field Theories and the Intersection Form

Details Discrete Quantum Field Theories and the Intersection Form Discrete Quantum Field Theories and the Intersection Form

1994-06-27

arxiv.org/abs/hep-th/9406173v1

Mod.Phys.Lett. A9 (1994) 2265-2271

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Latex, ITFA-94-19

Scientific paper

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 $\pm CP^{2}$, demonstrating non-triviality.

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