The Holographic Dictionary for Beta Functions of Multi-trace Coupling Constants

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.

31 pages. v2: added references. v3: added references, JHEP version

References in corpus (3)

• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• Large N Field Theory and AdS Tachyons
• Multitrace deformations, Gamow states, and Stability of AdS/CFT

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