Abstract
We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual (1+1)-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual AdS/CFT scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.
Highlights
As mentioned earlier in the usual AdS/C F T framework the holographic entanglement negativity for bipartite states in dual C F T1+1s could be characterized through the bulk entanglement wedge cross section (EWCS) as described in [35, 36]. The extension of this construction to flat holography is a significant issue which needs to be investigated. We address this outstanding issue and establish a novel construction for the bulk entanglement wedge and provide a definition for the EWCS in bulk asymptotically flat (2+1)-dimensional Einstein gravity and topologically massive gravity (TMG) dual to GC F T1+1s
In this article we have advanced a novel holographic construction to obtain the extremal entanglement wedge cross section (EWCS) for several bipartite pure and mixed states in GC F T1+1s located at the null infinity of the dual bulk (2+1)-dimensional asymptotically flat Einstein gravity and topologically massive gravity (TMG) theories
We have further proposed a prescription for the holographic entanglement negativity for the configuration in question by utilizing the EWCS obtained through the construction mentioned above
Summary
Quantum entanglement in extended many body systems has emerged as an exciting issue attracting intense research attention in the recent past across a diverse variety of disciplines. This interesting issue was investigated recently in [64] where an elegant and clear holographic characterization for the entanglement negativity of bipartite states in a class of GC F T1+1s dual to bulk asymptotically flat (2+1)-dimensional Einstein gravity and topologically massive gravity (TMG) was established Their construction involved specific algebraic sums of the lengths of extremal curves (HRT like surfaces termed swing surfaces [65]) homologous to certain combinations of intervals appropriate to the bipartite state in question. The holographic entanglement negativity computed through our construction matches up to an additive constant with the results described in [64] from the alternative proposal involving the algebraic sum of the lengths of specific combinations of bulk extremal curves as well as with the field theory replica technique results described in [56] in the large central charge limit This provides an extremely strong substantiation and consistency check for our construction of the bulk EWCS and the consequent computation for the entanglement negativity in the context of flat holography.
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