Negative complexity of formation: the compact dimensions strike back

Engelhardt, Netta; Folkestad, Åsmund

doi:10.1007/jhep07(2022)031

Title: Negative complexity of formation: the compact dimensions strike back

Journal Article · 05 July 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep07(2022)031 · OSTI ID:1907975

Engelhardt, Netta ^[1];

^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

We show that the vacuum-subtracted maximal volume, the proposed holographic dual to complexity of formation, can be negative when contributions from compact directions are included. We construct explicit solutions with arbitrarily negative complexity of formation in asymptotically AdS₄ × S⁷ SUGRA. These examples rely critically on the compact directions, specifically the fact that the full eleven-dimensional spacetime is not asymptotically AdS₁₁. While there is some ambiguity in the extension of the holographic complexity proposal to the compact directions, we show that the two natural candidates can both have arbitrarily negative complexity of formation in SUGRA solutions. We further find examples in which complexity can even decrease at late times, including cases of both single-sided geometries and two-sided wormholes. In particular, we construct a cosmological wormhole with simultaneously negative and decreasing complexity of formation (as computed by volume) at late times. We find a distinguished role for relevant primaries in these constructions and comment on possible interpretations.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0012567; SC0021886

OSTI ID:: 1907975

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 7 Vol. 2022; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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