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Quantum geometry of the universal hypermultiplet
Author(s) -
Ketov Sergei V.
Publication year - 2002
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/1521-3978(200209)50:8/9<909::aid-prop909>3.0.co;2-j
Subject(s) - instanton , moduli space , superstring theory , integrable system , physics , mathematical physics , type (biology) , space (punctuation) , metric (unit) , supersymmetry , mathematics , pure mathematics , operations management , economics , biology , ecology , linguistics , philosophy
The universal hypermultiplet moduli space metric in the type‐IIA superstring theory compactified on a Calabi‐Yau threefold is related to integrable systems. The instanton corrections in four dimensions arise due to multiple wrapping of BPS membranes and fivebranes around certain (supersymmetric) cycles of Calabi‐Yau. The exact (non‐perturbative) metrics can be calculated in the special cases of (i) the D‐instantons (or the wrapped D2‐branes) in the absence of fivebranes, and (ii) the fivebrane instantons with vanishing charges, in the absence of D‐instantons. The solutions of the first type are governed by the three‐dimensional Toda equation, whereas the solutions of the second type are governed by the particular Painlevé VI equation.