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 holographic description upto two derivative order for a matrix field theory which has no other operator with finite scaling dimension except for the energymomentum 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.
Highlights
Renormalization group (RG) flow describes how short distance fluctuations modify coupling constants as a system is probed at progressively larger length scales
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 holographic description upto two derivative order for a matrix field theory which has no other operator with finite scaling dimension except for the energymomentum tensor
Summary
Renormalization group (RG) flow describes how short distance fluctuations modify coupling constants (coupling functions in general) as a system is probed at progressively larger length scales. We 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. Let us consider a projected fixed point whose action S0[Φ] is made of single-trace operators in the D-dimensional Minkowski space.
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