  Puff field theories (PFT) arise as the decoupling limits of D3 branes in a
Melvin universe and exhibit spatially non-local dynamics. Unlike other
realizations of non-locality in string theory, PFTs have full SO(3) rotational
symmetry. In this work, we analyze the strongly coupled regime of a PFT through
gravitational holography. We find a novel mechanism at the heart of the
phenomenon of non-locality: a quantum entanglement of UV and IR dynamics. In
the holographic bulk, this translates to an apparent horizon splitting the
space into two regions - with the UV completion of the PFT sitting at the
horizon. We unravel this intricate UV-IR setting and devise a prescription for
computing correlators that extends the original dictionary of holographic
renormalization group. We then implement a cosmological scenario where PFT
correlators set the initial conditions for primordial fluctuations. We compute
the associated power spectrum of the CMB and find that the scenario allows for
a distinct stringy signature.
