Abstract
We consider averaged null energy conditions (ANEC) for strongly coupled quantum field theories in even (two and four) dimensional curved spacetimes by applying the no-bulk-shortcut principle in the context of the AdS/CFT duality. In the same context but in odd-dimensions, the present authors previously derived a conformally invariant averaged null energy condition (CANEC), which is a version of the ANEC with a certain weight function for conformal invariance. In even-dimensions, however, one has to deal with gravitational conformal anomalies, which make relevant formulas much more complicated than the odd-dimensional case. In two-dimensions, we derive the ANEC by applying the no-bulk-shortcut principle. In four-dimensions, we derive an inequality which essentially provides the lower-bound for the ANEC with a weight function. For this purpose, and also to get some geometric insights into gravitational conformal anomalies, we express the stress-energy formulas in terms of geometric quantities such as the expansions of boundary null geodesics and a quasi-local mass of the boundary geometry. We argue when the lowest bound is achieved and also discuss when the averaged value of the null energy can be negative, considering a simple example of a spatially compact universe with wormhole throat.
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ArXiv ePrint: 2008.07942
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Iizuka, N., Ishibashi, A. & Maeda, K. The averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality. J. High Energ. Phys. 2020, 106 (2020). https://doi.org/10.1007/JHEP10(2020)106
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DOI: https://doi.org/10.1007/JHEP10(2020)106