Abstract
Motivated by traversable wormhole constructions that require large amounts of negative energy, we explore constraints on the amount of negative energy that can be carried by a free Dirac field in a slab-shaped region between two parallel spatial planes. Specifically, we ask what is the minimum possible uniform energy density that can exist at some time, considering all possible states and all possibilities for the physics outside the slab. The vacuum state where we identify the two sides of the slab with antiperiodic boundary conditions gives one possible state with uniform negative energy, but we argue that states with more negative energy exist above 1+1 dimensions. Technically, we reduce the problem to studying a massive Dirac field on an interval in 1+1 dimensions and numerically search for states with uniform energy density in a lattice regulated model. We succeed in finding states with enhanced negative energy (relative to the antiperiodic vacuum) which also appear to have a sensible continuum limit. Our results for the mass-dependence of the minimum uniform energy density in 1+1 dimensions suggest that for a 3+1 dimensional massless Dirac fermion, it is possible to have states with arbitrarily large uniform negative energy density in an arbitrarily wide slab.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Faulkner, R.G. Leigh, O. Parrikar and H. Wang, Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition, JHEP 09 (2016) 038 [arXiv:1605.08072] [INSPIRE].
C.J. Fewster, Lectures on quantum energy inequalities, arXiv:1208.5399 [INSPIRE].
R. Bousso, Z. Fisher, S. Leichenauer and A.C. Wall, Quantum focusing conjecture, Phys. Rev. D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE].
R. Bousso et al., Proof of the Quantum Null Energy Condition, Phys. Rev. D 93 (2016) 024017 [arXiv:1509.02542] [INSPIRE].
A.C. Wall, Lower Bound on the Energy Density in Classical and Quantum Field Theories, Phys. Rev. Lett. 118 (2017) 151601 [arXiv:1701.03196] [INSPIRE].
S. Balakrishnan, T. Faulkner, Z.U. Khandker and H. Wang, A General Proof of the Quantum Null Energy Condition, JHEP 09 (2019) 020 [arXiv:1706.09432] [INSPIRE].
A. May, P. Simidzija and M. Van Raamsdonk, Negative energy enhancement in layered holographic conformal field theories, JHEP 08 (2021) 037 [arXiv:2103.14046] [INSPIRE].
M. Van Raamsdonk, Cosmology from confinement?, JHEP 03 (2022) 039 [arXiv:2102.05057] [INSPIRE].
S. Antonini, P. Simidzija, B. Swingle and M. Van Raamsdonk, Cosmology from the vacuum, arXiv:2203.11220 [INSPIRE].
T. Ishikawa, K. Nakayama and K. Suzuki, Casimir effect for lattice fermions, Phys. Lett. B 809 (2020) 135713 [arXiv:2005.10758] [INSPIRE].
T. Ishikawa, K. Nakayama and K. Suzuki, Lattice-fermionic Casimir effect and topological insulators, Phys. Rev. Res. 3 (2021) 023201 [arXiv:2012.11398] [INSPIRE].
Y.V. Mandlecha and R.V. Gavai, Lattice fermionic Casimir effect in a slab bag and universality, Phys. Lett. B 835 (2022) 137558 [arXiv:2207.00889] [INSPIRE].
S. Jarov and M. Van Raamsdonk, Allowed expectation values for general collections of observables, to appear.
J. Cardy and E. Tonni, Entanglement hamiltonians in two-dimensional conformal field theory, J. Stat. Mech. 1612 (2016) 123103 [arXiv:1608.01283] [INSPIRE].
E.E. Flanagan, Quantum inequalities in two-dimensional Minkowski space-time, Phys. Rev. D 56 (1997) 4922 [gr-qc/9706006] [INSPIRE].
D.N. Vollick, Quantum inequalities in curved two-dimensional space-times, Phys. Rev. D 61 (2000) 084022 [gr-qc/0001009] [INSPIRE].
C.J. Fewster and S. Hollands, Quantum energy inequalities in two-dimensional conformal field theory, Rev. Math. Phys. 17 (2005) 577 [math-ph/0412028] [INSPIRE].
Acknowledgments
We thank Stefano Antonini, Petar Simidzija, and Chris Waddell for collaboration on related topics and Felipe Rosso for discussions. We acknowledge support from the U.S. Department of Energy grant DE-SC0009986 (B.G.S.), the National Science and Engineering Research Council of Canada (NSERC) and the Simons foundation via a Simons Investigator Award and the “It From Qubit” collaboration grant.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2212.02609
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Swingle, B., Van Raamsdonk, M. Enhanced negative energy with a massless Dirac field. J. High Energ. Phys. 2023, 183 (2023). https://doi.org/10.1007/JHEP08(2023)183
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)183