Noncommutative Geometry in M-Theory and Conformal Field Theory

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In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the ... continued below

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Medium: P; Size: 171 pages

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Morariu, Bogdan May 1, 1999.

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Description

In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.

Physical Description

Medium: P; Size: 171 pages

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INIS; OSTI as DE00760324

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  • Other Information: TH: Thesis (Ph.D.); Submitted to the University of California, Department of Physics, Berkeley, CA (US)

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  • Report No.: LBNL--43407
  • Report No.: UCB-PTH-99/25
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 760324
  • Archival Resource Key: ark:/67531/metadc721285

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  • May 1, 1999

Added to The UNT Digital Library

  • Sept. 29, 2015, 5:31 a.m.

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  • April 4, 2016, 1:46 p.m.

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Morariu, Bogdan. Noncommutative Geometry in M-Theory and Conformal Field Theory, thesis or dissertation, May 1, 1999; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc721285/: accessed August 16, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.