Lattice Formulation of Two Dimensional Topological Field Theory

Details Lattice Formulation of Two Dimensional Topological Field Theory Lattice Formulation of Two Dimensional Topological Field Theory

2006-11-09

arxiv.org/abs/hep-lat/0611011v3

Prog.Theor.Phys.117:317-345,2007

Physics

High Energy Physics

High Energy Physics - Lattice

33 pages, 2 figures, references added, typos corrected

Scientific paper

10.1143/PTP.117.317

We investigate an integrable property and observables of 2 dimensional N=(4,4) topological field theory defined on a discrete lattice by using the "orbifolding" and "deconstruction" methods. We show that our lattice model possesses the integrability and the partition function reduces to matrix integrals of scalar fields on sites in consequence. We make clear meaningful differences between the discrete lattice and differentiable manifold, which would be important to a study of topological quantities on the lattice. We also propose a new construction of N=(2,2) supersymmetric lattice theory, which is realized by a suitable truncation of scalar fields from the N=(4,4) theory.

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