Large D-instanton effects in string theory

B. Pioline, S.J.G. Vandoren

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By reduction along the time direction, black holes in 4 dimensions yield instantons in 3 dimensions. Each of these instantons contributes individually at order exp(−|Q|/gs) to certain protected couplings in the three-dimensional effective action, but the number of distinct instantons is expected to be equal (or comparable) to the number of black hole micro-states, i.e. of order exp(Q2). The same phenomenon also occurs for certain protected couplings in four dimensions, such as the hypermultiplet metric in type II string theories compactified on a Calabi-Yau threefold. In either case, the D-instanton series is therefore asymptotic, much like the perturbative expansion in any quantum field theory. By using a Borel-type resummation method, adapted to the Gaussian growth of the D-instanton series, we find that the total D-instanton sum has an inherent ambiguity of order exp(−1/g2 s ). We further suggest that this ambiguity can be lifted by including Kaluza-Klein monopole or NS5-brane instantons.
Original languageUndefined/Unknown
Pages (from-to)008/1-008/11
Number of pages11
JournalJournal of High Energy Physics
Issue number07
Publication statusPublished - 2009

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