Summary
An attempt is made to balance the negative vacuum energy associated with the Freund-Rubin compactification of the 11-dimensional supergravity theory against the contribution from vacuum fluctuations. We do this in order to obtain a ground-state geometry which has four physical (flat) dimensions and is of the form (Minkowski)4×B 7, whereB 7 is one of the 7-dimensional manifoldsS 7,S 5×S 2,S 4×S 3, ⊂P 2×S 3,S 3×S 2×S 2 or theSU 3×SU 2×U 1 invariant spaces of Witten. We find that all of these solutions are unstable. As a side-issue the facility for computation of the particle spectra, which results from the use of light-cone gauge, is emphasized.
Riassunto
Si fa un tentativo di bilanciare l’energia negativa nel vuoto associata con la compattificazione di Freund-Rubin della teoria 11-dimensionale della supergravità rispetto al contributo delle fluttuazioni nel vuoto. Ciò allo scopo di ottenere una geometria dello stato fondamentale che ha quattro dimensioni fisiche (piatte) ed ha la forma (Minkowski)4×B 7, doveB 7 è uno dei multistrati a sette dimensioniS 7,S 5×S 2,S 4×S 3, ⊂P 2×S 3,S 3×S 2×S 2 o degli spazi invarianti di WittenSU 3×SU 2×U 1. Si trova che tutte queste soluzioni sono instabili. Come argomento collaterale si enfatizzano le modalità di calcolo degli spettri delle particelle, che risultano dall’uso del gauge del cono di luce.
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References
P. G. O. Freund andM. A. Rubin:Phys. Lett. B,94, 233 (1980).
E. Cremer, B. Julia andJ. Scherk:Phys.Lett. B,76, 409 (1978);E. Cremmer andB. Julia:Nucl. Phys. B,159, 141 (1979).
T. Horvath, L. Palla, E. Cremmer andJ. Scherk:Nucl. Phys. B,123, 57 (1979);S. Randjbar-Daemi andR. Percacci:Phys. Lett. B,117, 41 (1982);S. Randjbar-Daemi, Abdus Salam andJ. Strathdee:Nucl. Phys. B,114, 491 (1983);P. Candelas andS. Weinberg: Texas preprint UTTG-6-83, to appear inNucl. Phys. B.
C. A. Orzalesi andM. Pauri:Phys. Lett. B,107, 186 (1981);C. A. Orzalesi andM. J. Duff:Phys. Lett. B,122, 37 (1983);C. A. Orzalesi andG. Venturi: CERN preprint TH-3648-CERN (1983);J. S. Dowker: MC/TH/83-80, Manchester preprint;P. Candelas andD. J. Raine: Texas preprint (September 1983).
M. J. Duff, C. Pope andB. Nielson: Imperial College, London, preprint (1984);K. Ito andO. Yasuda: Tokyo preprint UT/426 (1984).
Abdus Salam andJ. Strathdee:Ann. Phys. (N. Y.),141, 316 (1982);J. Strathdee: ICTP, Trieste, Internal Report IC/83/3 (1983) (unpublished).
The tachyonic modes in the cases ofB 7=S 7 andB 7=S 4×S 3 had already been exhibited in the Addendum toS. Randjbar-Daemi, Abdus Salam andJ. Strathdee: ICTP, Trieste, preprint IC/83/226, to appear inNucl. Phys. B.
In this case the full spectrum has been worked out in the AdS 4 background.F. Englert andH. Nicolai: CERN preprint TH-3711 (1983);B. Biran, A. Casher, F. Englert, M. Rooman andP. Spindal:Phys. Lett. B,134, 179 (1984);E. Sezgin:Phys. Lett. B,138, 57 (1984)’scR. D’Auria andP. Fré: Torino preprint IFTT430 (1983);A. Casher, F. Englert, H. Nicolai andM. Rooman: CERN preprint TH-3794 (1984).
S. Randjbar-Daemi, Abdus Salam andJ. Strathdee: ICTP, Trieste preprint IC/84/13. The spaceB 7 (α, β, γ) are obtained from those of this paper by settingp=q=0 andr=1.
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Randjbar-Daemi, S., Salam, A. & Strathdee, J. Towards a self-consistent computation of vacuum energy in 11-dimensional supergravity. Nuov Cim B 84, 167–180 (1984). https://doi.org/10.1007/BF02721543
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DOI: https://doi.org/10.1007/BF02721543