Summary
A geometrical treatment of supersymmetric σ-models of ordinary and graded manifolds in given. The action is written in terms of differential forms on superspace, by means of a modified version of the Berezin duality operation. The linear sets associated to the models are explicitly exhibited and the «reduction» problem is discussed.
Riassunto
Si dà una trattazione geometrica dei modelli σ supersimmetrici su varietà ordinarie e graduate. Si scrive l'azione in termini di forme differenziali sul superspazio, per mezzo di una versione modificata dell'operazione di dualità proposta da Berezin. Si scrivono i sistemi lineari associati a questi modelli e si discute il problema della riduzione.
Резюме
Предлагается геометрическое рассмотрение суперсимметричных σ-моделей на обычных и сортированных множествах. Действие записывается в дуфференциальной форме на суперповерхности, используя модифицированный вариант действия дуальности Березина. В явном виде иллюстрируются линейные системы, связанные с рассмотренными моделями. Обсуждается проблема «приведения».
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References
P. Di Vecchia andS. Ferrara:Nucl. Phys. B,130, 93 (1977);E. Witten:Phys. Rev. D,16, 2991 (1977);O. Alvarez:Phys. Rev. D,17, 1123 (1978);R. Shankar andE. Witten:Phys. Rev. D,17, 2126 (1978);A. D'Adda, P. Di Vecchia andM. Luscher:Nucl. Phys. B,152, 125 (1979);A. V. Mikhailov andA. M. Perelomov:JETP Lett.,29, 445 (1979);I. Ya. Aref'eva, V. K. Krivoshchekov andP. B. Medvedev: Moscow preprint ITEP 173 (1978).
B. Zumino:Phys. Lett. B,87, 203 (1979).
A. V. Mikhailov:JETP Lett.,28, 512 (1978).
J. F. Schonfeld:Nucl. Phys. B,169, 49 (1980).
J. Lukierski:Lett. Math. Phys.,3, 135 (1979);Proceedings of the Symposium on Differential Geometric Models in Physics, Aix-en-Provence, 1979, Lecture Notes in Mathematics, Vol.836 (Berlin, 1980).
L. Girardello andS. Sciuto:Phys. Lett. B,77, 267 (1978);M. Chaichian andP. P. Kulish:Phys. Lett. B,78, 413 (1978).
S. Sciuto:Phys. Lett. B,90, 75 (1980).
R. D'Auria andS. Sciuto:Nucl. Phys. B,171, 189 (1980).
E. Napolitano andS. Sciuto: Torino preprint, IFTT 405 (1981).
A. N. Leznov, D. A. Leites andM. V. Savel'ev:Phys. Lett. B,96, 97 (1980).
F. A. Berezin:Sov. J. Nucl. Phys.,30, 605 (1979).
H. Eichenherr andM. Forger:Nucl. Phys. B,155, 381 (1979).
See, for instance,H. Flanders:Differential Forms (New York, N. Y., 1963).
V. E. Zakharov andA. V. Mikhailov:JETP Lett.,27, 42 (1978);Sov. Phys. JETP,47, 1017 (1978).
B. Zumino:Proceedings of the Conference on Gauge Theories and Modern Field Theory, Northeastern University, September 1975, edited byR. Arnowitt andP. Nath (Cambridge, Mass.).
F. A. Berezin:The Method of Second Quantization (New York, N. Y., 1966).
B. Zumino: lecture presented at theWorkshop on Unification of the Fundamental Interactions, Erice, March 17–24, 1980.
K. Pohlmeyer:Commun. Math. Phys.,46, 207 (1976).
E. Corrigan andC. Zachos: Caltech preprint CALT-68-727 (1979);T. Curtright: E. Fermi Institute preprint EFI 79/53 (1979);T. Curtright andC. Zachos: University of Wisconsin preprint COO-107 (1979);Z. Popowicz andLing-Lie Chau Wang:Phys. Lett. B,98, 253 (1981).
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Napolitano, E., Sciuto, S. Supersymmetric σ-models and graded Lie groups. Nuov Cim A 64, 406–420 (1981). https://doi.org/10.1007/BF02773435
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DOI: https://doi.org/10.1007/BF02773435