dc.contributor.author Koch, RDM en_US dc.contributor.author Ramgoolam, S en_US dc.date.accessioned 2016-04-01T15:03:04Z dc.date.submitted 2016-03-10T16:56:58.315Z dc.identifier.uri http://qmro.qmul.ac.uk/xmlui/handle/123456789/11614 dc.description 54 pages, 17 figures dc.description 54 pages, 17 figures en_US dc.description 54 pages, 17 figures en_US dc.description.abstract We show that correlators of the hermitian one-Matrix model with a general potential can be mapped to the counting of certain triples of permutations and hence to counting of holomorphic maps from world-sheet to sphere target with three branch points on the target. This allows the use of old matrix model results to derive new explicit formulae for a class of Hurwitz numbers. Holomorphic maps with three branch points are related, by Belyi's theorem, to curves and maps defined over algebraic numbers \$\bmQ\$. This shows that the string theory dual of the one-matrix model at generic couplings has worldsheets defined over the algebraic numbers and a target space \$ \mP^1 (\bmQ)\$. The absolute Galois group \$ Gal (\bmQ / \mQ) \$ acts on the Feynman diagrams of the 1-matrix model, which are related to Grothendieck's Dessins d'Enfants. Correlators of multi-matrix models are mapped to the counting of triples of permutations subject to equivalences defined by subgroups of the permutation groups. This is related to colorings of the edges of the Grothendieck Dessins. The colored-edge Dessins are useful as a tool for describing some known invariants of the \$ Gal (\bmQ / \mQ) \$ action on Grothendieck Dessins and for defining new invariants. en_US dc.subject hep-th en_US dc.subject hep-th en_US dc.subject math.NT en_US dc.title From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group en_US dc.type Internet Publication pubs.author-url http://arxiv.org/abs/1002.1634v1 en_US pubs.notes Not known en_US
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