1999/04/08 by Fedele Lizzi, Richard J. Szabo, Lizzi, Fedele +1 · 6 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Compactification (mathematics) #Diffeomorphism #Dirac operator #Duality (order theory) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry #High Energy Physics - Theory (hep-th) #Homogeneous space #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Non-critical string theory #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Operator algebra #Physics #Pure mathematics #Quantum Algebra (math.QA) #Quantum Chromodynamics and Particle Interactions #Quantum differential calculus #Quantum gravity #Quantum mechanics #Relationship between string theory and quantum field theory #Spectral triple #String duality #String theory #Worldsheet #gr-qc #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/9904064
published in arXiv (Cornell University) (Cornell University) · 17 pages, Latex2e, uses JHEP.cls (included); Based on talk given by the first author at the 6th Hellenic School and Workshop on Elementary Particle Physics, Corfu, Greece, September 6-26 1998. To be published in JHEP proceedings
arxiv created 1999/04/08 · openalex publication_date 1999/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A review of the applications of noncommutative geometry to a systematic formulation of duality symmetries in string theory is presented. The spectral triples associated with a lattice vertex operator algebra and the corresponding Dirac-Ramond operators are constructed and shown to naturally incorporate target space and discrete worldsheet dualities as isometries of the noncommutative space. The target space duality and diffeomorphism symmetries are shown to act as gauge transformations of the geometry. The connections with the noncommutative torus and Matrix Theory compactifications are also discussed.