Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Bulk Localized State and New Holographic Renormalization Group Flow in
  3D Spin-3 Gravity   We construct a localized state of a scalar field in 3D spin-3 gravity. 3D
spin-3 gravity is thought to be holographically dual to W$_3$ extended CFT on a
boundary at infinity. It is known that while W$_3$ algebra is a non-linear
algebra, in the limit of large central charge $c$ a linear finite-dimensional
subalgebra generated by $W_n \, (n=0,\pm1,\pm2)$ and $L_n (n= 0,\pm1)$ is
singled out. The localized state is constructed in terms of these generators.
To write down an equation of motion for a scalar field which is satisfied by
this localized state it is necessary to introduce new variables for an internal
space $\alpha^{\pm}$, $\beta^{\pm}$, $\gamma$, in addition to ordinary
coordinates $x^{\pm}$ and $y$. The higher-dimensional space, which combines the
bulk spacetime with the `internal space', which is an analog of superspace in
supersymmetric theory, is introduced. The `physical bulk spacetime' is a 3D
hypersurface with constant $\alpha^{\pm}$, $\beta^{\pm}$ and $\gamma$ embedded
in this space. We will work in Poincar\'e coordinates of AdS space and consider
W-quasi-primary operators $\Phi_{h}(x^+)$ with a conformal weight $h$ in the
boundary and study two and three point functions of W-quasi-primary operators
transformed as $e^{ix^+L^h_{-1}} e^{\beta^+W^h_{-1}} \Phi_{h}(0)
e^{-\beta^+W^h_{-1}}e^{-ix^+L^h_{-1}}$. Here $L^h_n$ and $W^h_n$ are sl(3,R)
generators in the hyperbolic basis for Poincar\'e coordinates. It is shown that
in the $\beta^+ \rightarrow \infty$ limit, the conformal weight changes to a
new value $h'=h/2$. This may be regarded as a Renormalization Group (RG) flow.
It is argued that this RG flow will be triggered by terms $\Delta S \propto
\beta^+ W^h_{-1}+\beta^- \overline{W}^h_{-1}$ added to the action.

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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph