Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions

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dc.creatorAoki, Hajime
dc.creatorNishimura, Jun
dc.creatorSusaki, Yoshiaki
dc.date2008-10-29
dc.date2009-04-23
dc.date.accessioned2026-07-07T13:07:05Z
dc.date.available2026-07-07T13:07:05Z
dc.descriptionWe present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our formulation is based on the algebraic characterization of the configuration space. This enables us to describe the twisted boundary conditions in terms of finite matrices and hence to realize the Morita equivalence at a fully regularized level. Matter fields in the fundamental representation turn out to be represented by rectangular matrices for twisted boundary conditions analogously to the matrix spherical harmonics on the fuzzy sphere with the monopole background. The corresponding Ginsparg-Wilson Dirac operator defines an index, which can be used to classify gauge field configurations into topological sectors. We also perform Monte Carlo calculations for the index as a consistency check. Our formulation is expected to be useful for applications of non-commutative geometry to various problems related to topological aspects of field theories and string theories.
dc.description25 pages, 2 figures v2: 2 figures added, version published in JHEP
dc.identifierhttps://arxiv.org/abs/0810.5234
dc.identifierhttp://arxiv.org/abs/0810.5234
dc.identifierJHEP 0904:055,2009
dc.identifierdoi:10.1088/1126-6708/2009/04/055
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227979
dc.subjectHigh Energy Physics - Theory
dc.subjectHigh Energy Physics - Lattice
dc.titleFinite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
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