Quantum Renormalization Group and Holography

Abstract

Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the Einstein gravity emerges as a long wavelength holographic description for a matrix field theory which has no other operator with finite scaling dimension except for the energy-momentum tensor. We also point out that holographic actions for general large N matrix field theories respect the inversion symmetry along the radial direction in the bulk if the beta functions of single-trace operators are gradient flows with respect to the target space metric set by the beta functions of double-trace operators.

5 pages; 1 figure; v2) references added

References in corpus (4)

• Exact evolution equation for the effective potential
• On the Extra Mode and Inconsistency of Horava Gravity
• Background independent holographic description : From matrix field theory to quantum gravity
• Holographic description of large N gauge theory

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