Geometric encoding of renormalization group $\beta -$functions in an emergent holographic dual description

Abstract

First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG $\beta -$functions of coupling functions and RG flow equation of the order-parameter field appear in the resulting effective action explicitly through the extra dimensional space. Second, we consider an effective dual holographic description derived recently, where the classical gravity theory of the large $N$ limit takes into account quantum corrections in the all-loop order. This non-perturbative nature turns out to originate from an intertwined renormalization structure between both RG flow equations of coupling functions and order-parameter fields in the emergent extra-dimensional space, where the IR boundary condition of the order-parameter field gives rise to a mean-field equation with fully renormalized interaction coefficients. Third, comparing the RG-reformulated effective field theory with this effective dual holographic description, we obtain term-by-term matching conditions in the level of an effective action. As a result, we express all RG coefficients of fields and interaction vertices in terms of the metric tensor of the dual holographic theory. Through this metric reformulation for the RG analysis, we propose a prescription on how to find RG $\beta -$functions of interaction coefficients in a non-perturbative way beyond the perturbative RG analysis. In particular, we claim that the present prescription of the RG flow generalizes the holographic RG flow of the holographic duality conjecture towards the absence of conformal symmetry, where the emergent holographic dual effective field theory has been derived from the first principle, thus being applicable even away from quantum criticality.

References in corpus (11)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Holography from Conformal Field Theory
• AdS_4/CFT_3 Construction from Collective Fields
• Einstein's Equations from Varying Complexity
• Holographic dual of free field theory
• Ricci flow and black holes
• Some Applications of Ricci Flow in Physics
• Background independent holographic description : From matrix field theory to quantum gravity
• Entanglement entropy and the Ricci flow
• Higher Spin Holography, RG, and the Light Cone
• Emergent geometry in recursive renormalization group transformations

Cited by in corpus (9)

• Emergent geometry in recursive renormalization group transformations
• Emergent dual holographic description as a non-perturbative generalization of the Wilsonian renormalization group
• Emergent dual holographic description for interacting Dirac fermions in the large $N$ limit
• Entanglement transfer from quantum matter to classical geometry in an emergent holographic dual description of a scalar field theory
• Beyond quantum chaos in emergent dual holography
• Nonequilibrium thermodynamics perspectives for the monotonicity of the renormalization group flow
• Renormalization group flow to effective quantum mechanics at IR in an emergent dual holographic description for spontaneous chiral symmetry breaking
• Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear $\sigma$ model
• Comparison between renormalization group derived emergent dual holography and string theory based holographic duality