String quartet no.27 in D major, op.20, no.4 / F. J. Haydn -- String quartet no.5, sz.102, BB110 / Bela Bartok -- String quartet in C minor, op.51, no.1 / Johannes Brahms / text

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This work is principally concerned with the operator approach to the orbifold compactification of the bosonic string. Of particular importance to operator formalism is the con formal structure and the operator product expansion. These are introduced and discussed in detail. The Frenkel-Kac-Segal mechanism is then examined and is shown to be a consequence of the duality of dimension one operators of an analytic bosonic string compactified on a certain torus. Possible generalizations to higher dimension operators are discussed, this includes the cross-bracket algebra which plays a central role in the vertex operator representation of Griess's algebra, and hence the Fischer-Griess Monster Group. The mechanism of compactification is then extended to orbifolds. The exposition includes a detailed account of the twisted sectors, especially of the zero-modes and the twisted operator cocycles. The conformal structure, vertex operators and correlation functions for twisted strings are then introduced. This leads to a discussion of the vertex operators which represent the emission of untwisted states. It is shown how these operators generate Kac-Moody algebras in the twisted sectors. The vertex operators which insert twisted states are then constructed, and their role as intertwining operators is explained. Of particular importance in this discussion is the role of the operator cocycles, which are seen to be crucial for the correct working of the twisted string emission vertices. The previously established formalism is then applied in detail to the reflection twist. This includes an explicit representation of the twisted operator cocycles by elements of an appropriate Clifford algebra and the elucidation of the operator algebra of the twisted emission vertices, for the ground and first excited states in the twisted sector. This motivates the 'enhancement mechanism', a generalization of the Frenkel-Kac-Segal mechanism, involving twisted string emission vertices, in dimensions 8, 16 and 24. associated with rank 8 Lie algebras, rank 16 Lie algebras and the cross-bracket algebra for the Leech lattice, respectively. Some of the relevant characters of the 'enhanced" modules are determined, and the connection of the cross-bracket algebra to the phenomenon of 'Monstrous Moonshine' and the Monster Group is explained. Algebra enhancement is then discussed from the greatly simplified shifted picture and extensions to higher order twists are considered. Finally, a comparison of this work with other recent research is given. In particular, the connection with the path integral formalism and the extension to general asymmetric orbifolds is discussed. The possibility of reformulating the moonshine module in a 'covaxiant' twenty-six dimensional setting is also considered.

In this thesis we address the problem of supersymmetry breaking in four dimensional string theory. We derive an effective Lagrangian describing the low energy degrees of freedom including the Goldstone mode associated with the spontaneously broken R-symmetry when a gaugino condensate forms. We show the equivalence between our approach and those previously used for studying gaugino condensate in 4D string theory but we also show the need to include quantum effects due to the strong coupling constant in the hidden sector. We determine the vacuum structure of the complete scalar potential and show that supersymmetry is broken and a large mass hierarchy may develop with a single gaugino condensate. Realistic phenomenological values for the gauge coupling constant, unification scale and soft supersymmetric breaking terms can be obtained. Consistency with the minimal supersymmetric extension of the standard model requires the hidden gauge group to be SU(6) or SO(9).

In this thesis we present a novel scheme for calculating the bosonic string partition function on certain curved backgrounds related to Anti-de Sitter [AdS] space. We take the concept of a large expansion from nonlinear sigma models in particle physics and apply it to the bosonic string theory sigma model, where the analogous large dimensionless parameter is the dimension of the target space, D. We then perform a perturbative expansion in negative powers of D, rather than in positive powers of α/ι(^2)(the conventional expansion parameter).As a specific example of a curved geometry of interest, we focus on an example of the metric proposed by Polyakov [1] to describe the dynamics of the Wilson loop of pure SU(N) Yang-Mills theory, namely AdS space. Using heat kernel methods, we find that within the large-D scheme one can obtain different conditions for Weyl invariance than those found in [2]. This is because our scheme is valid for backgrounds where a is no longer small. In particular, we find that it is possible to have a dilaton that depends on the holographic coordinate only, provided one allows mixing of the ghost and matter sectors of the worldsheet theory. This field preserves Poincare invariance in the gauge theory, unlike the conventional dilaton. We also compute a simple string amplitude by constructing certain vertex operators for a scalar field in AdS, and discuss the consequences for the string spectrum.

Treatise (DMA) -- Florida State University, 2003. / Advisor: Karen Clarke, Florida State University, School of Music. Title and description from dissertation home page (viewed 11-17-03). Document formatted into pages; contains 102 pages. Includes biographical sketch. Includes bibliographical references.