Japan. J. Math. 4, 63--93 (2009)

Instanton partition functions and M-theory

N.A. Nekrasov

Abstract: 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.


* This article is based on the 5th Takagi Lectures that the author delivered at the University of Tokyo on October 4 and 5, 2008.