From 4D reduced supersymmetric Yang-Mills integrals to branched polymers [Elektronische Ressource] / vorgelegt von Marc Wattenberg

From 4DReduced SupersymmetricYang-Mills Integrals toBranched PolymersDissertationzur Erlangung des Doktorgradesan der Fakult¨at fu¨r Physikder Universit¨at Bielefeldvorgelegt vonMarc WattenbergOctober 2004’There are really four dimensions, three which we call thethree planes of Space, and a fourth, Time. There is, however,a tendency to draw an unreal distinction between the formerthree dimensions and the latter, because it happens that ourconsciousness moves intermittently in one direction along thelatter from the beginning to the end of our lives.’‘That,’ said a very young man, making spasmodic efforts torelight his cigar over the lamp; ‘that... very clear indeed.’H. G. Wells, The Time Machine, 1895Contents1 Introduction 11.1 General survey . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 From Yang-Mills gauge theory to Yang-Mills matrix models . . 21.3 Thesis plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 From the IIb Matrix Model to Branched Polymers 92.1 The IIb matrix model. . . . . . . . . . . . . . . . . . . . . . . . 92.2 One-loop approximation . . . . . . . . . . . . . . . . . . . . . . 112.2.1 Perturbative expansion . . . . . . . . . . . . . . . . . . . 122.2.2 Long distance dynamics . . . . . . . . . . . . . . . . . . 202.2.3 Short distances . . . . . . . . . . . . . . . . . . . . . . . 242.3 Polyakov-line operator within the branched polymer model . . . 252.3.