Moduli Spaces and Topological Quantum Field Theories
Generally covariant field theories have observables which are metric independent. Hence they are global invariants. Recently, a new class of such theories, the so called topological quantum field theories (TQFTs’), were introduced by E.Witten. Originally they were affiliated with Yang-Mills instantons (TYM),  sigma models (TSM), and gravity (TG). Later on they enveloped other domains of physical systems [5-8]. The main question is obviously whether the TQFT’s probe some physical phenomena or are they merely mathematical tools to study topological properties of certain bundles? The answer to this question is two-fold: (i) The observables of the TQFT span the cohomology ring on certain moduli spaces. These moduli spaces may be intimately related to physics. An example familiar to string theorists is the moduli space of Riemann surfaces. Another example is the moduli space of instantons. (ii) The possibility that the TQFT’s describe a generally covariant phase of some physical systems [1,8]. In this work we follow the first direction.
KeywordsModulus Space Zero Mode Cohomology Ring Exterior Derivative World Sheet
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