Critical Sp(N) models in 6 − ϵ dimensions and higher spin dS/CFT

Abstract

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 − ϵ dimensions at imaginary values of coupling constants. Using calculations up to three loop order, we develop ϵ 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 super-group OSp(1|2). This suggests the existence of OSp(1|2) symmetric CFTs in dimensions smaller than 6. We show that the 6 − ϵ expansions of the scaling dimensions and sphere free energy in our OSp(1|2) model are the same as in the q → 0 limit of the q-state Potts model.