Misc,
Critical \$Sp(N)\$ Models in \$6-\epsilon\$ Dimensions and Higher Spin dS/CFT
(Feb 25, 2015)
Abstract
Theories of anti-commuting scalar fields are non-unitary, but they are of
interest both in statistical mechanics and in studies of the higher spin de
Sitter/Conformal Field Theory correspondence. We consider an \$Sp(N)\$ invariant
theory of \$N\$ anti-commuting scalars and one commuting scalar, which has cubic
interactions and is renormalizable in 6 dimensions. For any even \$N\$ we find an
IR stable fixed point in \$6-\epsilon\$ dimensions at imaginary values of
coupling constants. Using calculations up to three loop order, we develop
\$\epsilon\$ expansions for several operator dimensions and for the sphere free
energy \$F\$. The conjectured \$F\$-theorem is obeyed in spite of the non-unitarity
of the theory. The \$1/N\$ expansion in the \$Sp(N)\$ theory is related to that in
the corresponding \$O(N)\$ symmetric theory by the change of sign of \$N\$. Our
results point to the existence of interacting non-unitary 5-dimensional CFTs
with \$Sp(N)\$ symmetry, where operator dimensions are real. We conjecture that
these CFTs are dual to the minimal higher spin theory in 6-dimensional de
Sitter space with Neumann future boundary conditions on the scalar field. For
\$N=2\$ we show that the IR fixed point possesses an enhanced global symmetry
given by the supergroup \$OSp(1|2)\$. This suggests the existence of \$OSp(1|2)\$
symmetric CFTs in dimensions smaller than 6.
