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AdS-CFT correspondence and a new positive energy conjecture for general relativity
Abstract
We examine the AdS-CFT correspondence when gauge theory is considered on a compactified space with supersymmetry-breaking boundary conditions. We find that the corresponding supergravity solution has a negative energy, in agreement with the expected negative Casimir energy in the field theory. The stability of the gauge theory would imply that this supergravity solution has minimum energy among all solutions with the same boundary conditions. Hence we are led to conjecture a new positive energy theorem for asymptotically locally anti--de Sitter spacetimes. We show that the candidate minimum energy solution is stable against all quadratic fluctuations of the metric.
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“While the ground state of the CFT on S d-1 is dual to the empty global AdS d+1 , the CFT ground state on R d-3 ×T 2 is expected to be dual to certain AdS soliton solution [12,60,61] .”
From Casimir energy and modularity in higher-dimensional conformal field theories (2023) · cites this paper as [60]
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“where c 1 is proportional to the thermal free energy (1.8) (see (2.9)), which is natural from the bulk due to the relation between the black brane (which dominates the canonical ensemble) and the AdS soliton by double Wick rotations [60].”
From Casimir energy and modularity in higher-dimensional conformal field theories (2023) · cites this paper as [60]
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“The energy density (in the non-compact R d-3 directions) for the AdS soliton is [60] E soliton = - r d 0 L 1 L 2 16πG N ℓ d+1 = - (4π) d-1 ℓ d-1 4d d G N L 2 L d-1 1 ,(5.39)”
From Casimir energy and modularity in higher-dimensional conformal field theories (2023) · cites this paper as [60]
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Cites
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Cited by
Surface terms as counterterms in the AdS-CFT correspondence
Emparan, R., Johnson, C. V., & Myers, R. C. (1999) · Physical Review D · doi:10.1103/physrevd.60.104001 · Cited by 703
Self-citationCosmology of codimension-two braneworlds
Cline, J. M., Descheneau, J., Giovannini, M., & Vinet, J. (2003) · Journal of High Energy Physics · doi:10.1088/1126-6708/2003/06/048 · Cited by 133
Dibitetto, G., Petri, N., & Schillo, M. (2020) · Journal of High Energy Physics · doi:10.1007/jhep08(2020)040 · Cited by 45
Conserved charges in general relativity
Aoki, S., Onogi, T., & Yokoyama, S. (2021) · International Journal of Modern Physics A · doi:10.1142/s0217751x21500986 · Cited by 34
Casimir energy and modularity in higher-dimensional conformal field theories
Luo, C., & Wang, Y. (2023) · Journal of High Energy Physics · doi:10.1007/jhep07(2023)028 · Cited by 27
Aoki, S., & Onogi, T. (2022) · International Journal of Modern Physics A · doi:10.1142/s0217751x22501299 · Cited by 12
Geometric conservation in curved spacetime and entropy
Aoki, S., Hidaka, Y., Kawana, K., & Shimada, K. (2025) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-14138-5 · Cited by 2
Arbitrarily negative energy for small Kaluza-Klein bubbles
Horowitz, G. T., & Lu, G. (. (2025) · Physical Review D · doi:10.1103/xmm8-7kv6 · Cited by 1
Self-citation
Metadata
- Authors
- Horowitz, G. T., & Myers, R. C.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1998-12-21
- Volume
- 59
- Issue
- 2
- ISSN
- 0556-2821
- 1089-4918
- Cited by
- 350
- References
- 8
- Language
- en
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