• DOI:10.1007/JHEP05(2015)031
• Corpus ID: 115167208

The holographic dictionary for Beta functions of multi-trace coupling constants

@article{Aharony2015TheHD,
  title={The holographic dictionary for Beta functions of multi-trace coupling constants},
  author={Ofer Aharony and Guy Gur-Ari and Nizan Klinghoffer},
  journal={Journal of High Energy Physics},
  year={2015},
  volume={2015},
  pages={1-29}
}

• O. Aharony, Guy Gur-Ari, Nizan Klinghoffer
• Published 27 January 2015
• Physics
• Journal of High Energy Physics

A bstractField theories with weakly coupled holographic duals, such as large N gauge theories, have a natural separation of their operators into ‘single-trace operators’ (dual to single-particle states) and ‘multi-trace operators’ (dual to multi-particle states). There are examples of large N gauge theories where the beta functions of single-trace coupling constants all vanish, but marginal multi-trace coupling constants have non-vanishing beta functions that spoil conformal invariance (even when all multi-trace coupling constants vanish). The holographic dual of such theories should be a classical solution in anti-de Sitter space, in which the boundary conditions that correspond to the multi-trace coupling constants depend on the cutoff scale, in a way that spoils conformal invariance. We argue that this is realized through specific bulk coupling constants that lead to a running of the multi-trace coupling constants. This fills a missing entry in the holographic dictionary.