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:
[1] | DOI: 10.1016/0370-2693(87)90896-3 · doi:10.1016/0370-2693(87)90896-3 |
[2] | DOI: 10.1103/PhysRevLett.62.2579 · doi:10.1103/PhysRevLett.62.2579 |
[3] | DOI: 10.1016/0370-2693(87)91272-X · Zbl 1156.81434 · doi:10.1016/0370-2693(87)91272-X |
[4] | DOI: 10.1016/0370-2693(86)91204-9 · doi:10.1016/0370-2693(86)91204-9 |
[5] | DOI: 10.1016/0370-2693(88)90852-0 · doi:10.1016/0370-2693(88)90852-0 |
[6] | DOI: 10.1016/0370-2693(81)90744-9 · doi:10.1016/0370-2693(81)90744-9 |
[7] | DOI: 10.1016/0370-2693(81)90744-9 · doi:10.1016/0370-2693(81)90744-9 |
[8] | DOI: 10.1016/0370-1573(82)90087-4 · Zbl 0578.22027 · doi:10.1016/0370-1573(82)90087-4 |
[9] | DOI: 10.1016/0550-3213(83)90490-X · doi:10.1016/0550-3213(83)90490-X |
[10] | DOI: 10.1016/0550-3213(87)90647-X · doi:10.1016/0550-3213(87)90647-X |
[11] | DOI: 10.1016/0550-3213(87)90647-X · doi:10.1016/0550-3213(87)90647-X |
[12] | DOI: 10.1016/0550-3213(87)90647-X · doi:10.1016/0550-3213(87)90647-X |
[13] | DOI: 10.1016/0550-3213(86)90177-X · doi:10.1016/0550-3213(86)90177-X |
[14] | DOI: 10.1007/BF01220994 · Zbl 0604.14016 · doi:10.1007/BF01220994 |
[15] | Belavin A. A., Sov. Phys. JETP 64 pp 214– (1986) |
[16] | Mumford D., Enseign. Math. 23 pp 39– (1977) |
[17] | DOI: 10.1017/S0027763000000337 · Zbl 0585.32031 · doi:10.1017/S0027763000000337 |
[18] | DOI: 10.1017/S0027763000000337 · Zbl 0585.32031 · doi:10.1017/S0027763000000337 |
[19] | DOI: 10.1017/S0027763000000337 · Zbl 0585.32031 · doi:10.1017/S0027763000000337 |
[20] | DOI: 10.1007/BF01169586 · Zbl 0558.53037 · doi:10.1007/BF01169586 |
[21] | DOI: 10.1512/iumj.1979.28.28025 · Zbl 0385.32018 · doi:10.1512/iumj.1979.28.28025 |
[22] | DOI: 10.1017/S0027763000015968 · Zbl 0296.14012 · doi:10.1017/S0027763000015968 |
[23] | DOI: 10.1017/S0027763000015968 · Zbl 0296.14012 · doi:10.1017/S0027763000015968 |
[24] | DOI: 10.1070/IM1979v013n03ABEH002076 · Zbl 0439.14002 · doi:10.1070/IM1979v013n03ABEH002076 |
[25] | DOI: 10.2307/2373939 · Zbl 0431.14005 · doi:10.2307/2373939 |
[26] | DOI: 10.2307/2373939 · Zbl 0431.14005 · doi:10.2307/2373939 |
[27] | DOI: 10.1007/BF01161608 · Zbl 0602.53042 · doi:10.1007/BF01161608 |
[28] | DOI: 10.1016/0550-3213(85)90602-9 · doi:10.1016/0550-3213(85)90602-9 |
[29] | DOI: 10.1016/0550-3213(85)90603-0 · doi:10.1016/0550-3213(85)90603-0 |
[30] | DOI: 10.1016/0550-3213(86)90449-9 · doi:10.1016/0550-3213(86)90449-9 |
[31] | DOI: 10.1016/0550-3213(86)90449-9 · doi:10.1016/0550-3213(86)90449-9 |
[32] | DOI: 10.1016/0550-3213(86)90449-9 · doi:10.1016/0550-3213(86)90449-9 |
[33] | DOI: 10.1016/0550-3213(87)90102-7 · doi:10.1016/0550-3213(87)90102-7 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.