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

Abstract

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. Exact quantization conditions for the spectral problem of the Fermi gas are then obtained from the vanishing of the theta function. 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.

arXiv comment37 pages, 6 figures, typos corrected, clarifications added

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• Conceptual Aspects of Gauge/Gravity Duality
• Solving M-theory with the Conformal Bootstrap
• Matrix models from operators and topological strings
• The exact Schur index of $\mathcal{N}=4$ SYM
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Finite N from Resurgent Large N
• Exact Instanton Expansion of ABJM Partition Function
• ABJM Membrane Instanton from Pole Cancellation Mechanism
• Airy Function and 4d Quantum Gravity
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• Chern-Simons Theory on Seifert Manifold and Matrix Model
• More Large $N$ limits of 3d gauge theories
• Resummations and Non-Perturbative Corrections
• Mass-deformed ABJ and ABJM theory, Meixner-Pollaczek polynomials, and $su(1,1)$ oscillators