Abstract
Field 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.
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ArXiv ePrint: 1501.06664
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Aharony, O., Gur-Ari, G. & Klinghoffer, N. The holographic dictionary for Beta functions of multi-trace coupling constants. J. High Energ. Phys. 2015, 31 (2015). https://doi.org/10.1007/JHEP05(2015)031
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DOI: https://doi.org/10.1007/JHEP05(2015)031