Scientific article
Open access

Exact results in N = 8 $$ \mathcal{N}=8 $$ Chern-Simons-matter theories and quantum geometry

Published inThe journal of high energy physics, vol. 1507, p. 011-050
  • Open Access - SCOAP3
Publication date2015

We show that, in ABJ(M) theories with N = 8 $$ \mathcal{N}=8 $$ 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.

  • Nonperturbative Effects
  • Topological Strings
  • Chern-Simons Theories
  • AdSCFT Correspondence
Citation (ISO format)
CODESIDO SANCHEZ, Santiago, GRASSI, Alba, MARINO BEIRAS, Marcos. Exact results in N = 8 $$ \mathcal{N}=8 $$ Chern-Simons-matter theories and quantum geometry. In: The journal of high energy physics, 2015, vol. 1507, p. 011–050. doi: 10.1007/JHEP07(2015)011
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Article (Published version)
ISSN of the journal1029-8479

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