Supersymmetry, twistors, and the Yang-Mills equations
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- by Michael Eastwood PDF
- Trans. Amer. Math. Soc. 301 (1987), 615-635 Request permission
Abstract:
This article investigates a supersymmetric proof due to Witten of the twistor description of general Yang-Mills fields due to Green, Isenberg, and Yasskin. In particular, some rigor is added and the rather complicated calculations are given in detail.References
- Marjorie Batchelor, The structure of supermanifolds, Trans. Amer. Math. Soc. 253 (1979), 329–338. MR 536951, DOI 10.1090/S0002-9947-1979-0536951-0
- N. P. Buchdahl, Analysis on analytic spaces and non-self-dual Yang-Mills fields, Trans. Amer. Math. Soc. 288 (1985), no. 2, 431–469. MR 776387, DOI 10.1090/S0002-9947-1985-0776387-3 M. G. Eastwood, Ambitwistors, Twistor Newsletter 9 (1979), 55-58.
- Michael G. Eastwood, Roger Penrose, and R. O. Wells Jr., Cohomology and massless fields, Comm. Math. Phys. 78 (1980/81), no. 3, 305–351. MR 603497
- Michael G. Eastwood, The generalized Penrose-Ward transform, Math. Proc. Cambridge Philos. Soc. 97 (1985), no. 1, 165–187. MR 764506, DOI 10.1017/S030500410006271X
- Michael Eastwood and Claude LeBrun, Thickening and supersymmetric extensions of complex manifolds, Amer. J. Math. 108 (1986), no. 5, 1177–1192. MR 859775, DOI 10.2307/2374601
- Alan Ferber, Supertwistors and conformal supersymmetry, Nuclear Phys. B 132 (1978), no. 1-2, 55–64. MR 495851, DOI 10.1016/0550-3213(78)90257-2
- Gerd Fischer, Complex analytic geometry, Lecture Notes in Mathematics, Vol. 538, Springer-Verlag, Berlin-New York, 1976. MR 0430286 P. S. Green, J. Isenberg, and P. B. Yasskin, Non-self-dual gauge fields, Phys. Lett. B 78 (1978), 462-464.
- Paul Green, On holomorphic graded manifolds, Proc. Amer. Math. Soc. 85 (1982), no. 4, 587–590. MR 660609, DOI 10.1090/S0002-9939-1982-0660609-6
- J. Harnad, J. Hurtubise, M. Légaré, and S. Shnider, Constraint equations and field equations in supersymmetric $N=3$ Yang-Mills theory, Nuclear Phys. B 256 (1985), no. 4, 609–620. MR 802589, DOI 10.1016/0550-3213(85)90410-9
- G. M. Henkin and Yu. I. Manin, Twistor description of classical Yang-Mills-Dirac fields, Phys. Lett. B 95 (1980), no. 3-4, 405–408. MR 590021, DOI 10.1016/0370-2693(80)90178-1
- Bertram Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975) Lecture Notes in Math., Vol. 570, Springer, Berlin, 1977, pp. 177–306. MR 0580292 Yu. I. Manin, Gauge fields and holomorphic geometry, J. Soviet Math. 21 (1983), 465-507.
- Roger Penrose, Applications of negative dimensional tensors, Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969) Academic Press, London, 1971, pp. 221–244. MR 0281657 —, Twistor theory, its aims and achievements, Quantum Gravity: An Oxford Symposium, Clarendon Press, Oxford, 1975, pp. 268-407.
- R. Penrose and R. S. Ward, Twistors for flat and curved space-time, General relativity and gravitation, Vol. 2, Plenum, New York-London, 1980, pp. 283–328. MR 617923
- Roger Penrose and Wolfgang Rindler, Spinors and space-time. Vol. 1, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984. Two-spinor calculus and relativistic fields. MR 776784, DOI 10.1017/CBO9780511564048
- Robert Pool, Yang-Mills fields and extension theory, Mem. Amer. Math. Soc. 65 (1987), no. 358, iv+63. MR 874083, DOI 10.1090/memo/0358 M. Roček, An introduction to superspace and supergravity, Superspace and Supergravity (Eds., S. W. Hawking and M. Roček), Cambridge Univ. Press, 1981, pp. 71-131.
- R. S. Ward, On self-dual gauge fields, Phys. Lett. A 61 (1977), no. 2, 81–82. MR 443823, DOI 10.1016/0375-9601(77)90842-8
- R. O. Wells Jr., Complex manifolds and mathematical physics, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 2, 296–336. MR 520077, DOI 10.1090/S0273-0979-1979-14596-8 —, Complex geometry in mathematical physics, Les Presses de l’Université de Montréal, 1982. E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. B 77 (1978), 394-398.
- Brian G. Wybourne, Symmetry principles and atomic spectroscopy, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1970. Including an appendix of tables by P. H. Butler. MR 0421392
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 301 (1987), 615-635
- MSC: Primary 32L25; Secondary 53C05, 53C80, 81E13
- DOI: https://doi.org/10.1090/S0002-9947-1987-0882706-1
- MathSciNet review: 882706