Index Theorems on Torsional Geometries

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dc.creatorKimura, Tetsuji
dc.date2007-04-17
dc.date2007-08-14
dc.date.accessioned2026-07-07T10:59:36Z
dc.date.available2026-07-07T10:59:36Z
dc.descriptionWe study various topological invariants on a torsional geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH = 0, which appears in string theory compactification scenarios. By using the identification between the Clifford algebra on the geometry and the canonical quantization condition of fermions in quantum mechanics, we construct N=1 quantum mechanical sigma model in the Hamiltonian formalism. We extend this model to N=2 system, equipped with the totally anti-symmetric tensor associated with the torsion on the target space geometry. Next we construct transition elements in the Lagrangian path integral formalism and apply them to the analyses of the Witten indices in supersymmetric systems. We explicitly show the formulation of the Dirac index on the torsional manifold which has already been studied. We also formulate the Euler characteristic and the Hirzebruch signature on the torsional manifold.
dc.description45 pages, the version to appear in JHEP
dc.identifierhttps://arxiv.org/abs/0704.2111
dc.identifierhttp://arxiv.org/abs/0704.2111
dc.identifierJHEP0708:048,2007
dc.identifierdoi:10.1088/1126-6708/2007/08/048
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/187458
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.titleIndex Theorems on Torsional Geometries
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