, Volume 4, Issue 1, pp 63-93
Date: 28 Mar 2009

Instanton partition functions and M-theory

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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.

Communicated by: Hiraku Nakajima
This article is based on the 5th Takagi Lectures that the author delivered at the University of Tokyo on October 4 and 5, 2008.