{
  "id": "1512.09055",
  "version": "v1",
  "published": "2015-12-30T18:43:06.000Z",
  "updated": "2015-12-30T18:43:06.000Z",
  "title": "Holography as a highly efficient RG flow II: An explicit construction",
  "authors": [
    "Nicolas Behr",
    "Ayan Mukhopadhyay"
  ],
  "comment": "1+51 pages; can be read independently of part 1 of this work, which has been revised recently to make a better interphase with this work",
  "categories": [
    "hep-th",
    "gr-qc"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-30T18:43:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicit construction",
      "collective variables",
      "highly efficient rg flow reproduces",
      "uv data",
      "background metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151209055B",
      "inspire": 1411634
    }
  }
}