Japanese Journal of Mathematics

, Volume 4, Issue 1, pp 63–93

Instanton partition functions and M-theory


DOI: 10.1007/s11537-009-0853-9

Cite this article as:
Nekrasov, N.A. Jpn. J. Math. (2009) 4: 63. doi:10.1007/s11537-009-0853-9


We discuss instanton partition functions in various spacetime dimensions. These partition functions capture some information about the spectrum of the supersymmetric gauge theories and their low-energy dynamics. Some of these theories can be defined microscopically only through string theory. Remarkably, they even know about the M-theory. Our conjectures include the identities between the generalization of the MacMahon formula and the character of M-theory, compactified down to 0 + 1 dimension.

Keywords and phrases:

instantons supersymmetry gauge theory string theory M-theory random partitions generating functions 

Mathematics Subject Classification (2000):

05A15 05A19 81T13 81T30 81T45 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2009

Authors and Affiliations

  1. 1.Institut des Hautes Études Scientifiques, Le Bois-MarieBures-sur-YvetteFrance

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