Titlebook: Strings, Conformal Fields, and M-Theory; Michio Kaku Textbook 2000Latest edition Springer Science+Business Media New York 2000 Second quan

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Topological Field Theoryield theory, or gives a valid description of our universe and a unification of all known quantum forces. The frustration is that string theory has been evolving backward, ever since its accidental discovery in 1968 by Veneziano and Suzuki, so its underlying geometry is totally unknown.

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Modular Invariance and the A—D—E Classificationnformal field theory. Thus, we need to add an extra constraint to fix the theory. The next constraint that we will impose is . [1], a powerful tool which will allow us to fix many of the features of a conformal field theory and which yields many new surprises.

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=2 SUSY and Parafermionsn acceptable four-dimensional phenomenology. Because, to any order in perturbation theory, the dimension of space-time seems perfectly stable, we must necessarily resort to nonperturbative methods to compactify the unwanted dimensions. However, our techniques for analyzing nonperturbative phenomena

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Yang-Baxter Relationt, at criticality, the detailed behavior of a statistical mechanical system gets washed out, and universality sets in. Since we have a complete classification of certain classes of conformal field theories, we should be able to catalog the models of statistical mechanics at criticality according to

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Toward a Classification of Conformal Field Theoriesify these vacuums using various techniques, with varying degrees of success. At present, no comprehensive classification scheme exists that gives us insight into the structure of these vacuums. In fact, it is still largely a mystery why conformal field theories behave as they do. There has been some

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Topological Field Theory be discovered, it is impossible to determine whether the theory predicts nonsense, and must be discarded as yet another failed attempt at a unified field theory, or gives a valid description of our universe and a unification of all known quantum forces. The frustration is that string theory has bee