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Understanding Higher-Spin Gravity through Bilocal Holography for Free Fermions
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We consider a simple theory of N free fermions in d dimensions with O\left(N\right) or U\left(N\right) symmetry. The singlet sector of this theory is expected from holography to be dual to the notoriously complicated Vasiliev gravity. By defining bilocal fields we find an explicit holographic mapping between the two theories, similar to what was done previously for scalars, which allows us to construct a quantum version of Vasiliev gravity, including loop (=1/N) corrections. Further more, such a mapping establishes a non-supersymmetric instance of the AdS/CFT duality.
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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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