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High Energy Physics - Theory, hep-th
Abstract:
We compute one loop free energy for D=4 Vasiliev higher spin gravities based
on Konstein-Vasiliev algebras hu(m;n|4), ho(m;n|4) or husp(m;n|4) and subject
to higher spin preserving boundary conditions, which are conjectured to be dual
to the U(N), O(N) or USp(N) singlet sectors, respectively, of free CFTs on the
boundary of $AdS_4$. Ordinary supersymmetric higher spin theories appear as
special cases of Konstein-Vasiliev theories, when the corresponding higher spin
algebra contains $OSp({\cal N}|4)$ as subalgebra. In $AdS_4$ with $S^3$
boundary, we use a modified spectral zeta function method, which avoids the
ambiguity arising from summing over infinite number of spins. We find that the
contribution of the infinite tower of bulk fermions vanishes. As a result, the
free energy is the sum of those which arise in type A and type B models with
internal symmetries, the known mismatch between the bulk and boundary free
energies for type B model persists, and ordinary supersymmetric higher spin
theories exhibit the mismatch as well. The only models that have a match are
type A models with internal symmetries, corresponding to $n=0$. The matching
requires identification of the inverse Newton's constant $G_N^{-1}$ with $N$
plus a proper integer as was found previously for special cases. In $AdS_4$
with $S^1\times S^2$ boundary, the bulk one loop free energies match those of
the dual free CFTs for arbitrary $m$ and $n$. We also show that a
supersymmetric double-trace deformation of free CFT based on OSp(1|4) does not
contribute to the ${\cal O}(N^0)$ free energy, as expected from the bulk.
