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Background independent holographic description : From matrix field theory to quantum gravity
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We propose a local renormalization group procedure where length scale is changed in spacetime dependent way. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical sources for low energy modes at each scale, we provide a prescription to derive background independent holographic duals for field theories. From a first principle construction, it is shown that the holographic theory dual to a D-dimensional matrix field theory is a (D+1)-dimensional quantum theory of gravity coupled with matter fields of various spins. The gravitational theory has (D+1) first-class constraints which generate local spacetime transformations in the bulk. The (D+1)-dimensional diffeomorphism invariance is a consequence of the freedom to choose different local RG schemes.
Forward citations
Cited by 3 Pith papers
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QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow
A framework called SymQRG identifies 3D quantum gravity as the symmetry-preserving RG flow of 2D CFTs, realized discretely by U_q(SL(2,R)) 6j symbols.
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$SO(1, d + 1)$ symmetry of the Exact RG equation
The ERG evolution operator is SO(1,d+1)-invariant for any admissible cutoff, with cutoff-dependent conformal generators that reduce to standard AdS isometries for the special AdS-mapping cutoff.
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Yang-Mills interaction from boundary vector model
The ERG flow of the USp(2N) singlet sector of a free 3D U(2N) scalar theory yields a bulk AdS4 cubic action that is on-shell equivalent to Yang-Mills plus a field-strength-cubed term.
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