The N = 8 superconformal bootstrap in three dimensions

Shai M. Chester, Jaehoon Lee, Silviu S. Pufu, Ran Yacoby

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108 Scopus citations

Abstract

We analyze the constraints imposed by unitarity and crossing symmetry on the four-point function of the stress-tensor multiplet of N = 8 superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that the OPE of the primary operator of the stress-tensor multiplet with itself must have parity symmetry. We then analyze the relations between the crossing equations, and we find that these equations are mostly redundant. We implement the independent crossing constraints numerically and find bounds on OPE coefficients and operator dimensions as a function of the stress-tensor central charge. To make contact with known N = 8 superconformal field theories, we compute this central charge in a few particular cases using supersymmetric localization. For limiting values of the central charge, our numerical bounds are nearly saturated by the large N limit of ABJM theory and also by the free U(1) × U(1) ABJM theory.

Original languageEnglish (US)
Article number143
JournalJournal of High Energy Physics
Volume2014
Issue number9
DOIs
StatePublished - Sep 2014

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Keywords

  • AdS-CFT Correspondence
  • Conformal and W Symmetry
  • Extended Supersymmetry

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