Emergent geometry in recursive renormalization group transformations

Abstract

Holographic duality conjecture has been proposed to be a novel non-perturbative theoretical framework for the description of strongly correlated electrons. However, the duality transformation is not specified to cause ambiguity in the application of this theoretical machinery to condensed matter physics. In this study, we propose a prescription for the holographic duality transformation. Based on recursive renormalization group (RG) transformations, we obtain an effective field theory, which manifests the RG flow of an effective action through the introduction of an extra dimension. Resorting to this prescription, we show that RG equations of all coupling constants are reformulated as emergent geometry with an extra dimension. We claim that the present prescription serves as microscopic foundation for the application of the holographic duality conjecture to condensed matter physics.

References in corpus (6)

• AdS_4/CFT_3 Construction from Collective Fields
• Einstein's Equations from Varying Complexity
• Holographic dual of free field theory
• Higher Spin Holography, RG, and the Light Cone
• Geometric encoding of renormalization group $\beta -$functions in an emergent holographic dual description
• Emergent dual holographic description for interacting Dirac fermions in the large $N$ limit

Cited by in corpus (10)

• Gravitational path integral from the $T^2$ deformation
• Geometric encoding of renormalization group $\beta -$functions in an emergent holographic dual description
• 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
• Nonequilibrium thermodynamics perspectives for the monotonicity of the renormalization group flow
• Beyond quantum chaos in emergent dual holography
• 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