21,259 research outputs found
N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
We construct four-dimensional N=4 super-Yang-Mills theories on a conic sphere
with various background R-symmetry gauge fields. We study free energy and
supersymmetric Renyi entropy using heat kernel method as well as localization
technique. We find that the universal contribution to the partition function in
the free field limit is the same as that in the strong coupling limit, which
implies that it may be protected by supersymmetry. Based on the fact that, the
conic sphere can be conformally mapped to and the R-symmetry
background fields can be supported by the R-charges of black hole, we propose
that the holographic dual of these theories are five-dimensional,
supersymmetric STU topological black holes. We demonstrate perfect agreement
between N=4 super-Yang-Mills theories in the planar limit and the STU
topological black holes.Comment: 1+48 pages, v2:typo fixed+references adde
Entanglement renormalization and integral geometry
We revisit the applications of integral geometry in AdS and argue that
the metric of the kinematic space can be realized as the entanglement contour,
which is defined as the additive entanglement density. From the renormalization
of the entanglement contour, we can holographically understand the operations
of disentangler and isometry in multi-scale entanglement renormalization
ansatz. Furthermore, a renormalization group equation of the long-distance
entanglement contour is then derived. We then generalize this integral
geometric construction to higher dimensions and in particular demonstrate how
it works in bulk space of homogeneity and isotropy.Comment: 40 pages, 7 figures. v2: discussions on the general measure added,
typos fixed; v3: sections reorganized, various points clarified, to appear in
JHE
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