To boost or not to boost, that's the question

Or should we talk about dS/CFT correspondence or dS/SFT correspondence in cosmological correlators? In non-unitary field theories – which are conjectured to be dual to cosmological correlators – scale invariance does not necessarily imply full conformal invariance. While general relativity predicts the emergence of conformal invariance (or boost symmetry in the bulk), various modified theories of gravity suggest only scale invariance, characterized by the absence of bulk boost symmetry. We demonstrate this distinction using Einstein-Aether theory as a canonical example.

💡 Research Summary

The paper investigates whether scale invariance in a holographic dual of an expanding universe necessarily entails full conformal invariance, focusing on the role of bulk boost symmetry. In unitary quantum field theories, the Zamolodchikov‑Polchinski theorem guarantees that a scale‑invariant theory is also conformally invariant because the trace of the stress tensor must be a total divergence of a virial current, which under unitarity can be removed. However, the holographic description of cosmological correlators (dS/CFT or dS/SFT) involves a Euclidean, non‑unitary dual theory, so the theorem does not apply. Consequently, a theory can be scale‑invariant while lacking special conformal transformations, which in the bulk correspond to spatial boosts.

To illustrate this possibility, the authors employ Einstein‑Aether theory, a modification of General Relativity that introduces a dynamical, unit‑norm timelike vector field (u^\mu). The action consists of the Einstein‑Hilbert term with cosmological constant plus a kinetic term for the aether field parameterized by four dimensionless couplings (c_i). The vector field defines a preferred frame, breaking Lorentz invariance at the fundamental level.

A de Sitter background in the Poincaré patch is considered: \