# Exact results in N=8 Chern-Simons-matter theories and quantum geometry

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Santiago Codesido, Alba Grassi, Marcos Mariño

**5/9/14**Published in : arXiv:1409.1799

In this paper, we show that, in ABJ(M) theories with N=8 supersymmetry, the non-perturbative sector of the partition function on the three-sphere simplifies drastically. Due to this simplification, we are able to write closed form expressions for the grand potential of these theories, which determines the full large N asymptotics. Moreover, we find explicit formulae for the generating functionals of their partition functions, for all values of the rank N of the gauge group. They involve Jacobi theta functions on the spectral curve associated to the planar limit. We also show that the partition function, as a function of N, can be extended in a natural way to an entire function on the full complex plane, and we explore some possible consequences of this fact for the quantum geometry of M-theory and for putative de Sitter extensions.