A geometric approach to the path integral formalism of p-branes. (English) Zbl 0726.58013
Summary: The configuration space for a path integral description of a p-brane is seen as a vector bundle over moduli spaces. The Einstein condition, applied to such vector bundles over compact Kähler manifolds, provides the required stability conditions. Consequently moduli spaces for such extended objects of higher dimensionality are constructed. Finally a Hermitian metric can be introduced in these moduli spaces.
MSC:
| 58D27 | Moduli problems for differential geometric structures |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 53C80 | Applications of global differential geometry to the sciences |
| 32L81 | Applications of holomorphic fiber spaces to the sciences |
| 32Q20 | Kähler-Einstein manifolds |
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
| 32G81 | Applications of deformations of analytic structures to the sciences |
| 58D30 | Applications of manifolds of mappings to the sciences |
Keywords:
string theory; Belavin-Knizhnik theorem; configuration space; path integral description; vector bundle over moduli spaces; Einstein condition; Hermitian metricReferences:
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