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Cited by 214Black Holes and Theoretical PhysicsCosmology and Gravitation TheoriesQuantum Electrodynamics and Casimir Effect

The DOI matches its Crossref record; 43 of the 44 references it cites were found in a registry or an index; none of the 22 sources its claims cite is checked for support yet.

Casimir energy and radius stabilization in five and six dimensional orbifolds

Open access
Pontón, Eduardo, Poppitz, Erich·2001·Journal of High Energy Physics
DOI 10.1088/1126-6708/2001/06/019
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TL;DR

The paper computes one-loop Casimir energies on five- and six-dimensional orbifolds and studies whether they can stabilize the compactification radius. It finds that massless-field Casimir energy alone is typically repulsive in the motivated models, but brane-localized kinetic terms, massive fields, and tuned brane/cosmological counterterms can produce minima.

Key findings

  • For \(S^1/Z_2\), neglecting fixed-point terms, the Casimir energy is one half that of \(S^1\). The massless periodic scalar result is \(V_{+,{\rm scalar}}(\phi)=-\frac{3\zeta(5)}{64\pi^2}\frac{1}{\phi^2 L^4}\), with ratios \(V_{+,{\rm graviton}}=5V_{+,{\rm scalar}}\), \(V_{+,{\rm fermion}}=-4V_{+,{\rm scalar}}\), \(V_{+,{\rm vector}}=3V_{+,{\rm scalar}}\), \(V_{+,{\rm gravitino}}=-8V_{+,{\rm scalar}}\); antiperiodic scalar gives \(V_{-,{\rm scalar}}=-\frac{15}{16}V_{+,{\rm scalar}}\) and antiperiodic fermion \(V_{-,{\rm fermion}}=\frac{15}{4}V_{+,{\rm scalar}}\).
  • Massive fields can stabilize the radius if their Casimir contribution is repulsive and dominates at small radii, while the massless contribution is attractive and the bulk cosmological constant is fine-tuned positive; the radius is then typically of order the inverse mass.
  • Brane-localized kinetic terms can also stabilize the radion. With one boundary term vanishing, a minimum occurs at a radius of order the nonzero \(c_i\); with both present, a local minimum persists for asymmetry \(c_0/c_L\sim 0.3\), but there is no minimum if \(c_0=c_L\). NDA-sized terms can yield a radius several times the cutoff, and larger terms can yield a larger radius while perturbation theory remains consistent.
  • In the 6D toroidal case, for repulsive total Casimir energy the fixed-area minimum is at \(\tau=e^{2\pi i/3}\). Applying the results to the 5D supersymmetric model of ref. [22], the massless-field radion potential is repulsive, \(V_{\rm massless}(\phi)=-1364V_{+,{\rm scalar}}(\phi)=+\frac{1023\zeta(5)}{16}\frac{1}{\phi^2 L^4}\); a stable minimum with vanishing cosmological constant requires positive bulk cosmological constant and negative brane tensions, which appears problematic for supersymmetry.

Methods

  • One-loop Casimir energies are computed using \(\zeta\)-function regularization on \(S^1/Z_2\) and \(T^2/Z_k\) orbifolds, for gravitational, massless, and massive fields with periodic or antiperiodic boundary conditions.
  • The radius potential is analyzed including bulk cosmological constant, brane-tension counterterms, and brane-localized kinetic/mass terms; normalization conditions \(V(\phi)=V'(\phi)=0\) are imposed to seek minima with vanishing four-dimensional cosmological constant.
  • An exact tree-level propagator with brane kinetic terms is derived to check perturbativity, and the general results are applied to the 5D supersymmetric electroweak model of ref. [22] and the 6D composite-Higgs model of ref. [23].

Limitations

  • The paper states that it neglects warping/backreaction from brane tensions and bulk cosmological constant counterterms, assumes brane tensions are small enough, and treats only static minima; cosmological evolution is left for future work.
  • It states that deciding whether the required stabilization is viable in the supersymmetric 5D case requires a full embedding in 5D supergravity, since the needed bulk counterterm is not supersymmetric in the simplest 5D supergravities.
  • The text also notes that the field-theory orbifolds considered cannot at present be derived from known string constructions and are treated only as low-energy effective theories up to a cutoff; additionally, the 5D SUSY model has a second degenerate minimum at \(\phi=\infty\), and for negative bulk cosmological constant the true minimum would be AdS, raising tunneling concerns.

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Integrity signals

Registry

Crossref · 10.1088/1126-6708/2001/06/019

Cites

43 of 43 references verified0 citation errors · 0 not checkable

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Citations

Cites

Show all 44 references

Research works printed but not linked: 7

  1. Th. Kaluza, Zum Unitätsproblem der Physik, Sitzungber. d. Berl. Akad. 966 1921, reprinted in Modern Kaluza-Klein theories, T. Appelquist, A. Chodos and P.G. Fre- und, eds., Addison-Wessley Reading, USA 1987.
  2. O. Klein, Quantum theory and five-dimensional relativity, Z. Phys. 37 (1926) 895-906; reprinted in Modern Kaluza-Klein theories, T. Appelquist, A. Chodos and P.G. Freund eds., Addison-Wessley Reading, USA 1987.
  3. D.J. Toms, Quantized bulk fields in the Randall-Sundrum compactificat¡ion model, hep-th/0005189; · arXiv
  4. N. D. Birrell and P. C. Davies, Quantum Fields In Curved Space, Cambridge Univ. Pr., Cambridge 1982.
  5. P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Springer New York, USA 1997.
  6. A. Losev, G. Moore and S.L. Shatashvili, M & m's, Nucl. Phys. B 522 (1998) 105 [hep-th/9707250]. · arXiv
  7. E. Elizalde, S.D. Odintsov, A. Romeo, A.A. Bytsenko, and S. Zerbini, Zeta Regular- ization Techniques with Applications, World Scientific, Singapore 1994.

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Metadata

Authors
Pontón, E., & Poppitz, E.
Affiliations
Yale University (US)
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2001-06-08
Volume
2001
Issue
06
Pages
019-019
ISSN
1029-8479 (ISSN-L)
DOI
10.1088/1126-6708/2001/06/019
OpenAlex
W2026481067
Cited by
210
References
44
Citations by year
2026: 7 · 2025: 3 · 2024: 5 · 2023: 5 · 2022: 6 · 2021: 7 · 2020: 8 · 2019: 2 · 2018: 5 · 2017: 3 · 2016: 2 · 2015: 6 · 2014: 10 · 2013: 7 · 2012: 1
FWCI
8.86
Type
journal article
Language
en
Open access
Locations
  • Journal of High Energy Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Funders
U.S. Department of Energy (DE‐FG02‐, DEFG0292ER40704)
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Electrodynamics and Casimir Effect
Keywords
Casimir energy, radius stabilization, orbifolds, one-loop effective action, boundary conditions, fixed points, cosmological constant, brane tension

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