New mechanism for nonlocality from string theory: UV-IR quantum entanglement and its imprints on the CMB

Puff field theories (PFT) arise as the decoupling limits of D3 branes in a Melvin universe and exhibit spatially nonlocal dynamics. Unlike other realizations of nonlocality 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 nonlocality: 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 cosmic microwave background and find that the scenario allows for a distinct stringy signature.

Figure 1

The Ricci scalar for the bulk spacetime dual to the PFT as a function of the holographic coordinate $\xi$. The throat referred to in the text appears at $\xi ={\xi }_0=2^{-1/6}$.

Figure 2

Convergence rate $\Theta$ of future-directed null geodesics projected away from $\xi ={\xi }_0$ surface.

Figure 3

A cartoon of the covariant entanglement proposal of 15, 16. The $\Theta =0$ entanglement screen separates the bulk into two regions A and B, and the boundary into two regions $a$ and $b$. It is proposed that the entanglement entropy of region a or b is given by the area of entanglement screen.

Figure 4

Oscillating spacelike geodesics with $P=0.7$ in the $\xi -X$ plane. The length of the segment labeled (A) is denoted in the text by $l_{{\xi }_1}^{ir}(P)$; the length of the segment (B) is denoted by $l_{{\xi }_2}^{uv}(P)$.

Figure 5

Log-log plot of Eq. (34) relating the turn-around critical point ${\xi }_{cr}$ to momentum $P$.

Figure 6

Log-log plots of the various UV-IR relations described in the text.

Figure 7

Length of spacelike geodesics as a function of momentum $P$. Note that at maximum momentum $P_m$ the length is finite and given by $l_{cr}$.

Figure 8

Various correlation functions as a function of $P$. Note that there is a finite value for the correlators at $P=P_m$.

Figure 9

A rough cartoon of cosmological history through an inflationary epoch. The dotted lines delineate a red-shifted momentum window while the Hubble scale is shown as a solid line.

Figure 10

A semilog plot of the normalized power spectrum with initial conditions set by the correlators of the PFT. We have chosen $\nu =-1$ (de Sitter inflation), $G={10}^{24}$, and $\Delta ={10}^{-2}$. The horizontal dotted line corresponds to a scale invariant spectrum. The vertical dotted line corresponds to $k\sim G^{-1/3}{\Delta }^{-1}$.

Figure 11

C-functions for the various theories considered in this appendix.

Figure 12

$\Theta$ for the various theories considered in this appendix.

Figure 13

Displacement $\Delta X$ of spacelike geodesics as a function of momentum $P$.

Figure 14

Geodesics for a sequence of displacements.

Figure 15

(a) Plot of geodesic lengths from Dijkstra’s algorithm along $\xi ={\xi }_0$; (b) Minimum length paths from Dijkstra’s algorithm.