Spacetime from unentanglement

Abstract

The past decade has seen a tremendous effort toward unraveling the relationship between entanglement and emergent spacetime. These investigations have revealed that entanglement between holographic degrees of freedom is crucial for the existence of bulk spacetime. We examine this connection from the other end of the entanglement spectrum and clarify the assertion that maximally entangled states have no reconstructable spacetime. To do so, we first define the conditions for bulk reconstructability. Under these terms, we scrutinize two cases of maximally entangled holographic states. One is the familiar example of AdS black holes; these are dual to thermal states of the boundary conformal field theory. Sending the temperature to the cutoff scale makes the state maximally entangled and the respective black hole consumes the spacetime. We then examine the de Sitter limit of Friedmann-Robertson-Walker (FRW) spacetimes. This limit is maximally entangled if one formulates the boundary theory on the holographic screen. Paralleling the anti-de Sitter (AdS) black hole, we find the resulting reconstructable region of spacetime vanishes. Motivated by these results, we prove a theorem showing that maximally entangled states have no reconstructable spacetime. Evidently, the emergence of spacetime is endemic to intermediate entanglement. By studying the manner in which intermediate entanglement is achieved, we uncover important properties about the boundary theory of FRW spacetimes. With this clarified understanding, our final discussion elucidates the natural way in which holographic Hilbert spaces may house states dual to different geometries. This paper provides a coherent picture clarifying the link between spacetime and entanglement and develops many promising avenues of further work.

Spacetime and universal soft modes: Black holes and beyond

“…There are, however, several proposals aiming toward it. In particular, a description based on a holographic screen seems promising for describing cosmological de Sitter spacetime [34,47], at least when the spacetime deviates-even slightly-from the pure de Sitter vacuum (e.g. by the existence of another energy component beyond the cosmological constant).…”

An inverse seesaw model with $U(1)_R$ gauge symmetry

“…The scalar and gauge sector are the same as in Ref. [55] where U (1) R gauge boson mass is given by VEV of ϕ and new gauge coupling…”

“…The inverse seesaw mechanism requires a left-handed neutral fermions S L in addition to the right-handed ones N R , and provides us more complicated neutrino mass matrix which can make mass hierarchies softer than the other models such as canonical seesaw [46][47][48][49] and provide rich phenomenologies such as unitarity constraints [50,51]. The U (1) R symmetry requires three SM singlet fermions with non-zero U (1) R charge to cancel gauge anomaly [52][53][54][55][56] and forbid unnecessary Yukawa interactions to obtain inverse seesaw mechanism. We then assign A 4 triplet representation to S L and N R , and some relevant Yukawa couplings are written in terms of modular form providing a constrained 1 Some reviews are useful to understand the non-Abelian group and its applications to flavor structure [34][35][36][37][38][39][40][41].…”

Gauged $$U(1)_{L_\mu -L_\tau }$$ scotogenic model in light of $$R_{K^{(*)}}$$ anomaly and AMS-02 positron excess

“…The contradiction is then relaxed due to new available annihilation channels via exchanging of gauge or Higgs boson associated with the U (1) group. Particularly, comparing with gauged U (1) B−L model [7], gauged U (1) Lµ−Lτ model [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]) has less stringent constraints due to the fact that corresponding gauge boson Z does not couple to SM quarks and electron directly. It is worthy to note that a light Z ∼ O(100) MeV with gauge coupling g ∼ 10 −3 is suitable to interpret the muon g − 2 anomaly [24,25].…”