Gravitational action with null boundaries

By Luis Lehner, R. Myers, E. Poisson, Rafael D. Sorkin. 2016

366 citations recorded by the source corpus.

The present paper provides a complete treatment of boundary terms in general relativity to include cases with lightlike boundary segments along with the usual spacelike and timelike ones. Applications of this exhaustive treatment includes a recent conjecture on computational complexity in the context of AdS/CFT.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/81c46857744e620a34b9b042ce1e8d9acb7decba

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Citations in the corpus

Complexity of formation in holography (2016, methodology): “gravitational action for null boundary surfaces and for joints where such null boundaries intersect with other boundary surfaces [16].”
Comments on holographic complexity (2016, methodology): “We have adopted slightly different conventions in appendix A than originally presented in [14].”
On the time dependence of holographic complexity (2017, methodology): “We will now add the boundary counterterm to the action, which was introduced in [25] to make the action invariant under the reparametrizations of null boundaries of the WDW patch.”
Noether charge, black hole volume, and complexity (2016, methodology): “8) (The algebraic details are found again in [38]).”
Circuit complexity in quantum field theory (2017, background): “In the latter case, the logarithmic factor came from joint terms [17] in the gravitational action, and the ambiguity arose from the freedom to choose the normalization of the null normals on the boundary of the WDW patch.”
Circuit complexity for free fermions (2018, background): “ similar logarithmic factor was found in the leading divergence in the holographic complexity [12] for the complexity=action proposal. In the latter case, the logarithmic factor came from joint terms [9] in the gravitational action, and the argument of the logarithm was ambiguous because of the free”
Holographic complexity in Vaidya spacetimes. Part I (2018, methodology): “As discussed in [33], there are inherent ambiguities in calculating the gravitational action for regions delimited by null boundaries.”
On volumes of subregions in holography and complexity (2016, background): “The gravitational action is composed of a bulk term, a null-boundary term, and a corner term (for more details see [43, 44, 67]):”
Circuit complexity for coherent states (2018, background): “ cuto, and dis the spacetime dimension of the boundary theory. The scale ‘is undetermined and arises because of ambiguities in dening the gravitational action on regions with null boundary segments [23,39]. An analogous ambiguity appears in evaluating the complexity for the scalar eld theory because”
Holographic complexity in Vaidya spacetimes. Part II (2018, methodology): “section of two timelike or spacelike boundary segments and which are dened in terms of the \boost angle" 7We noticed a typo in the null surface contribution to the action, proportional to , in [33,35]. Correcting for this mistake, we have ipped the sign of the term above. We comment further on ”
Superboost transitions, refraction memory and super-Lorentz charge algebra (2018, background): “We do not provide a covariant formulation of this boundary term, or the boundary terms Y μν , which would require geometrical tools on boundary null surfaces [53–56] or a prescription from holographic renormalization [57, 58].”
Complexity and entanglement for thermofield double states (2018, methodology): “ also classify this as part of the previous discrepancy in the constant of proportionality (between the complexity and the entropy), i.e., 49This expression includes a counter term introduced in ref. [26] in order to restore the reparametrization invariance of the gravitational action and which was ”
Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “where I WDW contains the important boundary contributions coming from the null boundaries of the WDW patch MWDW , also including the joint contributions coming from the intersections of the null boundaries [31].”
Divergences in holographic complexity (2016, background): “While this action is diffeomorphism invariant under changes of coordinates in the bulk and on the timelike and spacelike boundaries, [8] show that it depends on the choice of coordinate λ on the null boundary components.”