Abstract
We review the construction of extended ( N = 2 and N = 4 ) superconformal algebras over triple systems and the gauged WZW models invariant under them. The N = 2 superconformal algebras (SCA) realized over Freudenthal triple systems (FTS) admit extension to “maximal” N = 4 SCA's with SU(2) × SU(2) × U(1) symmetry. A detailed study of the construction and classification of N = 2 and N = 4 SCA's over Freudenthal triple systems is given. We conclude with a study and classification of gauged WZW models with N = 4 superconformal symmetry.
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References
M. Green, J. H. Schwarz and E. Witten, “Superstring Theory”, Cambridge Univ. Press, (1987, Cambridge).
T. Banks, L. Dixon, D. Friedan and E. Martinec, Nucl. Phys. B299 (1988) 613.
W. Boucher, D. Friedan and A. Kent, Phys. Lett. 172B (1986) 316; P. DiVecchia, J.L. Petersen and M. Yu, Phys. Lett. 172B (1986) 211; A.B. Zamolodchikov and V.A. Fateev, Zh. Eksp. Theor. Fiz. 90 (1986) 1553 and Sov. Phys. JETP 6 (1985) 215; Z. Qiu, Phys. Lett. 188B (1987) 207; D. Gepner and Z. Qiu, Nucl. Phys. B285 (1987) 423
W. Lerche, C. Vafa and N.P. Warner, Nucl. Phys. B324 (1989) 427.
Y. Kazama and H. Suzuki, Nucl. Phys. bf B321 (1989) 232; Phys. Lett. B216 (1989) 112
L.J. Dixon, J. Lykken and M.E. Peskin, Nucl. Phys. B325 (1989) 329.
I. Bars, Nucl. Phys. B334 (1990) 125
N. Seiberg, Nucl. Phys. B303 (1988) 286.
See P. Fendley, W. Lerche, S. D. Mathur and N.P. Warner, “N=2 Supersymmetric Integrable Models from Affine Toda Theories”, Preprint CTP1865 (CALT-68-1631; HUTP-90/A036) and the references therein.
E. Witten, Nucl. Phys. B340 (1990) 281; E. Witten, Comm. Math. Phys. 118 (1988) 411; C. Vafa, Harvard Preprint HUTP-90/A064; J. Distler and P. Nelson, Phys. Rev. Lett. 66 (1991) 1955; R. Dijkgraaf, H. Verlinde and E. Verlinde, Preprint PUPT-1217 (IASSNS-HEP-90/80 ).
P. Goddard, A. Kent and D. Olive, Phys. Lett. 152B (1985) 88; Comm. Math. Phys. 103 (1986)105; P. Goddard, W. Nahm and D. Olive, Phys. Lett. 160B (1985) 111.
H. Sugawara, Phys. Rev. 170 (1968) 1659; C. Sommerfield, Phys. Rev. 176 (1968) 2019.
M. Günaydin, Phys. Lett. B255 (1991) 46.
M. Günaydin and S. Hyun, Mod. Phys. Lett. A6 (1991) 1733.
M. Günaydin and S. Hyun, Nucl. Phys. B373 (1992) 688.
K. Schoutens, Nucl. Phys. B295 (1988) 634; A. Sevrin, W. Troost and A. Van Proeyen, Phys. Lett. B208 (1988) 447.
M. Günaydin, “Ternary Algebraic Approach to Extended Superconformal Symmetry”, invited talk to appear in the proceedings of the Vth Regional Conference on Mathematical Physics, Trakya University, Edirne, Türkiye, Dec. 1991.
M. Günaydin, Int. Jour. Mod. Phys. A8 (1993) 301.
M. Günaydin, Phys. Rev. D47 (1993) 3600.
J. Tits, Nederl. Akad. van Wetens. 65 (1962) 530; I. L. Kantor, Sov. Math. Dok. 5 (1964) 1404; M. Koecher, Amer. J. Math. 89 (1967) 787.
I.L. Kantor, Trudy Sem. Vektor. Anal. 16 (1972) 407; Sov. Math. Dokl. 14 (1973) 254.
I. Bars and M. Günaydin, J. Math. Phys. 20 (1979) 1977.
H. Freudenthal, Proc. Konikl.Nederl. Akad. Wet. Ser. A57 (1954) 218–230 and 363–408; K. Meyberg, ibid A71 (1968) 162–174 and 175–190.
I.L. Kantor and I.M. Skopets,Sel. Math. Sov. 2 (1982)293.
P. Goddard and A. Schwimmer, Phys. Lett. B214 (1988) 209.
M. Günaydin, J.L. Petersen, A. Taormina and A. Van Proeyen, Nucl. Phys. B322 (1989)402.
V.G. Knizhnik, Theor. Math. Phys. 66 (1986) 68.
M. Bershadsky, Phys.Lett., 174B (1986) 285.
A. Van Proeyen, Class. Quantum Gravity, 6 (1989) 1501; A. Sevrin and G. Theodoridis, Nucl. Phys.,B332 (1990) 380.
E. Guadagnini, M. Martellini and M. Minchev, Phys.Lett., B191 (1987) 69; W. Nahm, “Gauging Symmetries of Two Dimensional Conformally Invariant Models”, Davis Preprint, UCD-88-02 (unpublished); M. R. Douglas, “G/H Conformal Theory”, Ph.D. Thesis, Caltech (1988), unpublished; A. Altschuler, K. Bardakci and E. Rabinovici, Comm. Math. Phys.,118(1988) 157; D. Karabali, Q.H. Park H. J. Schnitzer and Z. Yang, Phys.Lett.,B216 (1989) 307; D. Karabali and H. J. Schnitzer, Nucl. Phys., B329(1990) 649; K. Gawedzki and A. Kupiainen Phys.Lett.,B215(1988) 119; Nucl. Phys.,B320(1989) 649; P. Bowcock, Nucl. Phys.,B316 (1989) 80.
E. Witten, Comm. Math. Phys.,144 (1992) 189.
R. Rohm, Phys. Rev. D32 (1984) 2849.
P. Di Vecchia, V.G. Knizhnik, J.L. Petersen and P. Rossi, Nucl. Phys. B253 (1985) 701.
A. Sevrin, W. Troost, A. Van Proeyen and Ph. Spindel, Nucl. Phys.,B308 (1988) 662.
H. J. Schnitzer, Nucl. Phys.,B324 (1989) 412.
E. Witten, Nucl. Phys., B371 (1992) 191.
J. Wess and B. Zumino, Phys.Lett., B37 (1971) 95.
E. Witten, Comm. Math. Phys., 92 (1984) 455.
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Günaydin, M. (1995). Extended superconformal symmetry, Freudenthal triple systems and gauged WZW models. In: Aktaş, G., Saçlioğlu, C., Serdaroğlu, M. (eds) Strings and Symmetries. Lecture Notes in Physics, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59163-X_255
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DOI: https://doi.org/10.1007/3-540-59163-X_255
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