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Holographic and Wilsonian renormalization groups. (English) Zbl 1298.81181
Summary: We develop parallels between the holographic renormalization group in the bulk and the Wilsonian renormalization group in the dual field theory. Our philosophy differs from most previous work on the holographic RG; the most notable feature is the key role of multi-trace operators. We work out the forms of various single-and double-trace flows. The key question, ‘what cutoff on the field theory corresponds to a radial cutoff in the bulk?’ is left unanswered, but by sharpening the analogy between the two sides we identify possible directions.

81T13 Yang-Mills and other gauge theories in quantum field theory
81V17 Gravitational interaction in quantum theory
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T17 Renormalization group methods applied to problems in quantum field theory
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