Nonunitary CFTs in Higher Dimensions

Nonunitary conformal field theories (CFTs) are of interest in various areas of theoretical physics. In the context of statistical physics, for example, it was demonstrated a long time ago by Fisher that critical φ^3 theory in d=6-ε spacetime dimensions can be used to study the Yang-Lee edge singularity. Additionally, nonunitary CFTs with anticommuting scalar fields have emerged as natural candidates for a dual description of higher-spin Vasiliev theories in de Sitter space, giving rise to the so called dS/CFT correspondence. Motivated by these observations, we will describe field theoretic results indicating that there exist interacting nonunitary CFTs with anticommuting scalar fields in spacetime dimensions higher than 6. A distinctive feature of these CFTs is that they have real couplings and positive operator dimensions, despite the fact that the lack unitarity. We will propose a formulation of these CFTs in terms of the 6+ε expansion of φ^3 theory, and provide evidence that an alternative formulation may be obtained using the well-known critical O(N) models with anticommuting scalar fields in the 4+ε expansion. We will also explore critical O(N) models with the usual commuting scalar fields across various spacetime dimensions, and present surprising new formulations of these CFTs in odd dimensions. The talk will be based mainly on arXiv:1508.03639 and upcoming work with Hugh Osborn. Other relevant references include arXiv:1404.1094, arXiv:1502.07271, and arXiv:1512.04443.