Grand Partition Functions of Little Matrix Models with ABCD - High Energy Physics - TheoryReport as inadecuate

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Abstract: Itoyama-Tokura type USp matrix model is discussed. Non-Abelian Berry-s phasesin a T-dualized model of IT model were reconsidered. These phases describe thehigher dimensional monopoles; Yang monopole and nine-dimensional monopole. Theyare described by the connections of the BPST instanton on S^4 and theTchrakian-GKS instanton on S^8, respectively. As a preparation to understandtheir effect in original zero-dimensional model, we consider partition functionof simplified matrix models. We compute partition functions of SU, SO and USpreduced matrix models. Groups SO and USp appear in low energy effectivetheories of string against orientifold background. In this evaluation we chosedifferent poles from that of Moore-Nekrasov-Shatashvili and our previousresult. The position of poles explain branes- and the orientifold-sconfigurations. There is a brane which is sitting on the orientifold in theSO2N model, while in USp2N and SO2N+1 model there are no branes on theorientifold. The grand partition functions of these models are considered. Theyfollow to linear second order ordinary differential equations and theirsingularities are q=0,\infty. Their solutions can be analytically continued towhole q plane. We show the expectation values of the number N of A and C casesas examples. There is an ambiguity coming from the problem on sign. Grandpartition functions with minus sign give effective actions which have cuspsingularities.

Author: Hironobu Kihara


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