期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 7, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP07(2015)011
关键词
Nonperturbative Effects; Topological Strings; Chern-Simons Theories; AdSCFT Correspondence
资金
- National Research Foundation (Korea)
- Fonds National Suisse [200020-137523, 200020-141329]
- NCCR SwissMAP
- Swiss National Science Foundation (SNF) [200020_141329, 200020_137523] Funding Source: Swiss National Science Foundation (SNF)
We show that, in ABJ(M) theories with N = 8 supersymmetry, the nonperturbative 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.
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