Entwinement and the emergence of spacetime

Abstract

It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by "internal", possibly gauged, degrees of freedom that are not spatially organized, and that can give rise to gaps smaller than the inverse size of the system. In a holographic context, such small gaps are associated to the appearance of horizons and singularities in the dual spacetime. Here, we propose a concept of entwinement, which is intended to capture this fine structure of the wavefunction. Holographically, entwinement probes the entanglement shadow -the region of spacetime not probed by the minimal surfaces that compute spatial entanglement in the dual field theory. We consider the simplest example of this scenario -a 2d conformal field theory (CFT) that is dual to a conical defect in AdS 3 space. Following our previous work, we show that spatial entanglement in the CFT reproduces spacetime geometry up to a finite distance from the conical defect. We then show that the interior geometry up to the defect can be reconstructed from entwinement that is sensitive to the discretely gauged, fractionated degrees of freedom of the CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical defect geometry, suggesting a potential quantum information theoretic meaning for these objects in a holographic context. These results may be relevant for the reconstruction of black hole interiors from a dual field theory.

Holographic dictionary and defects in the bulk

“…Moreover, this formula coincides with the two-point correlator in the orbifold CFT obtained by usual image method [13,32]. Thus, in the orbifold case we have a full agreement of GKPW, geodesic and CFT computations.…”

“…In this case the spacetime is a conical orbifold AdS 3 /Z N . It is important to note that the boundary of this spacetime preserves asymptotic Virasoro symmetry [13,31]. In our case, one can show that in this case a sum over images emerges naturally:…”

“…The dynamics of the bulk objects described by these solutions is almost trivial in a sense that it can only be innately realized in the action of the identification Γ, or it can be induced by acting with isometries (such e. g. as Lorentzian symmetry) on the basic static configurations. Yet this underwhelming at first sight picture is still highly useful in the holographic approach for study of problems such as the thermalization problem [4][5][6][7][8][9], entanglement physics [10][11][12][13], chaos in QFT [14]. Moreover, there are also many powerful analytic method suitable for studying the 2D CFT on the boundary.…”

Holographic dual of a time machine

“…First of all, we have to understand how to interpret the boundary state dual to the DeDeo-Gott geometry, whether this quantum state is pathological or just an exotic yet physical state. From the boundary point of view a single conical defect, if its angular deficit is α ¼ 2πð1 − 1=NÞ, can be thought of as state created by a nonlocal twist operator in a conformal field theory [41,[47][48][49][50][51]. But what it means to have such an interplay of two independently boosted defects has to be clarified.…”

“…These issues will be commented further on, but the general point of view described in this section remains unchanged. 2 This idea of windings, or entwinements, in holography has been introduced in [41], but there it was related to a concept of entanglement entropy "shadows" rather than to subleading contributions to the propagator.…”