A contour integral representation for the dual five-point function and a symmetry of the genus-4 surface in
| Autor: | Ji-Ping Sha, Andrew J. Hanson |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Surface (mathematics)
Pure mathematics Dual resonance model 010308 nuclear & particles physics Analytic continuation 010102 general mathematics General Physics and Astronomy Statistical and Nonlinear Physics Function (mathematics) Symmetry group 01 natural sciences Methods of contour integration Genus (mathematics) 0103 physical sciences 0101 mathematics Symmetry (geometry) Mathematical Physics Mathematics |
| Zdroj: | Journal of Physics A: Mathematical and General. 39:2509-2537 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/39/10/017 |
| Popis: | The invention of the "dual resonance model" N-point functions BN motivated the development of current string theory. The simplest of these models, the four-point function B4, is the classical Euler Beta function. Many standard methods of complex analysis in a single variable have been applied to elucidate the properties of the Euler Beta function, leading, for example, to analytic continuation formulas such as the contour-integral representation obtained by Pochhammer in 1890. Here we explore the geometry underlying the dual five-point function B5, the simplest generalization of the Euler Beta function. Analyzing the B5 integrand leads to a polyhedral structure for the five-crosscap surface, embedded in RP5, that has 12 pentagonal faces and a symmetry group of order 120 in PGL(6). We find a Pochhammer-like representation for B5 that is a contour integral along a surface of genus five. The symmetric embedding of the five-crosscap surface in RP5 is doubly covered by a symmetric embedding of the surface of genus four in R6 that has a polyhedral structure with 24 pentagonal faces and a symmetry group of order 240 in O(6). The methods appear generalizable to all N, and the resulting structures seem to be related to associahedra in arbitrary dimensions. |
| Databáze: | OpenAIRE |
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