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Article overview
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Holography as a highly efficient RG flow II: An explicit construction | Nicolas Behr
; Ayan Mukhopadhyay
; | Date: |
30 Dec 2015 | Abstract: | We complete the reformulation of the holographic correspondence as a
emph{highly efficient RG flow} that can also determine the UV data in the
field theory in the strong coupling and large $N$ limit. We introduce a special
way to define operators at any given scale in terms of appropriate
coarse-grained collective variables, without requiring the use of the
elementary fields. The Wilsonian construction is generalised by promoting the
cut-off to a functional of these collective variables. We impose three criteria
to determine the coarse-graining. The first criterion is that the effective
Ward identities for local conservation of energy, momentum, etc. should
preserve their standard forms, but in new scale-dependent background metric and
sources which are functionals of the effective single trace operators. The
second criterion is that the scale-evolution equations of the operators in the
actual background metric should be state-independent, implying that the
collective variables should not explicitly appear in them. The final required
criterion is that the endpoint of the scale-evolution of the RG flow can be
transformed to a fixed point corresponding to familiar non-relativistic
equations with a finite number of parameters, such as incompressible
non-relativistic Navier-Stokes, under a certain universal rescaling of the
scale and of the time coordinate. Using previous work, we explicitly show that
in the hydrodynamic limit each such highly efficient RG flow reproduces a
unique classical gravity theory with precise UV data that satisfy our IR
criterion and also lead to regular horizons in the dual geometries. We obtain
the explicit coarse-graining which reproduces Einstein’s equations. Finally, we
show how our construction can be interpolated with the traditional Wilsonian RG
flow at a suitable scale, and can be used to develop new non-perturbative
frameworks for QCD-like theories. | Source: | arXiv, 1512.9055 | Services: | Forum | Review | PDF | Favorites |
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