Abstract
We use the complexity equals action proposal to calculate the rate of complexity growth for field theories that are the holographic duals of asymptotically flat spacetimes. To this aim, we evaluate the on-shell action of asymptotically flat spacetime on the Wheeler-DeWitt patch. This results in the same expression as can be found by taking the flat-space limit from the corresponding formula related to the asymptotically AdS spacetimes. For the bulk dimensions that are greater than three, the rate of complexity growth at late times approaches from above to Lloyd's bound. However, for the three-dimensional bulks, this rate is a constant and differs from Lloyd's bound by a logarithmic term.
Highlights
It was proposed in [1,2] that the holographic dual of asymptotically flat spacetimes in d þ 1 dimensions is a d-dimensional field theory that has Bondi-Metzner-Sachs (BMS) symmetry
In this paper we calculate the rate of complexity growth for BMSFTd
Since the final formulas for the growth rate are given by taking the flat space limit from the anti–de Sitter (AdS)=conformal field theory (CFT) calculation, we can check the results of various potential regions
Summary
It was proposed in [1,2] that the holographic dual of asymptotically flat spacetimes in d þ 1 dimensions is a d-dimensional field theory that has Bondi-Metzner-Sachs (BMS) symmetry. The boundary complexity is given by the bulk gravitational action that is evaluated on a region of spacetime known as the Wheeler-DeWitt (WDW) path It is a portion of space-time bounded by null surfaces anchored at the related time on the boundary. The background geometries that we use in this paper are asymptotically flat two-sided black holes in spacetime dimensions greater than three and two-sided FSC in three dimensions All of these geometries are given by taking the flat-space limit from their corresponding asymptotically AdS counterparts.
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