2006/11/21 by Kazutoshi Ohta, Tomohisa Takimi · 23 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Gauge theory #Integrable system #Lattice (music) #Lattice field theory #Lattice model (finance) #Mathematical physics #Mathematics #Observable #Physics #Quantum #Quantum chaos and dynamical systems #Quantum field theory #Quantum gravity #Quantum mechanics #Scalar field #Scalar field theory #Theoretical physics #Topological quantum number #Topology (electrical circuits) #hep-lat #hep-th
paper · pdf · doi:10.1143/ptp.117.317
published in Progress of Theoretical Physics 117(2), 317-345 (Oxford University Press) · 33 pages, 2 figures, references added, typos corrected
arxiv created 2006/11/21 · openalex publication_date 2007/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate an integrable property and the observables of 2-dimensional = (4,4) topological field theory defined on a discrete lattice by using the “orbifolding” and “deconstruction” methods. We show that our lattice model is integrable and, for this reason, the partition function reduces to matrix integrals of scalar fields on the lattice sites. We elucidate meaningful differences between a discrete lattice and a differentiable manifold. This is important for studying topological quantities on a lattice. We also propose a new construction of = (2,2) supersymmetric lattice theory, which is realized through a suitable truncation of scalar fields from the = (4,4) theory.