Abstract
We make use of Chern-Simons cohomology and the family index theorem to deal with two-dimensional anomalies, infinite-dimensional algebras and their relations. We also take advantage of Zweibein formulation to treat the world sheet trace anomaly and Virasoro algebra in Polyakov string and to show how the anaomaly-free condition gives rise to the critical dimensions.
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References
Polyakov, A. M., Phys. Lett. 103B, 207 (1981); Friedan, D., in Recent Developments in Field Theory and Statistical Mechanics, North-Holland, Amsterdam; Alvarez, O., in Vertex Operators in Mathematics and Physics, Springer-Verlag, N.Y., 1984.
Banks, T. and Peskin, M. E., ‘Gauge Invariance of String Fields’, preprint SLAC-PUB-3740, July, 1985.
Friedan, D., Qiu, Z. and Shenker, S., in Vertex Operators in Mathematics and Physics, Springer-Verlag, N.Y., 1984.
Segal, C., Commun. Math. Phys. 80, 301 (1981).
Mickelsson, J., Commun. Math. Phys. 97, 361 (1985).
Faddeev, L. D., Phys. Lett. 145B, 81 (1984).
Zoller, D. J., ‘Cocycle and the Virasoro Algebra’, preprint, 1985.
Alvarez, O., ‘Conformal Anomalies and the Index Theorem’, preprint, UCB-PTH-85/39.
Reiman, A. G., Seacenov-Tyan-Shanskii, M. A., and Faddeev, L. D., Func. Anal. Appl. 18, 319 (1984); Guo, H. Y., Wu, K., and Wang, S. K., Comm. Theor. Phys. (Beijing) 4, 113 (1985); Zumino, B., in W. A. Bardeen and A. R. White (eds.), Symposium on Anomalies Geometry, Topology, World Scientific 1985; R. Jackiw, ibid. H. Y. Guo, ibid. Y. S. Wu, ibid.
Atiyah, M. F. and Singer, I. M., Proc. Nat. Acad. Sci. 81, 2597 (1984); Alvarez, O., Singer, I. M., and Zumino, B., Commun. Math. Phys. 96, 409 (1984); Alvarez-Gaume, L. and Ginsparg, P., Nucl. Phys. B243, 449 (1984);
Wess, J. and Zumino, B., Phys. Lett. 37B, 95 (1971).
Christ, N. H., Friedberg, R., and Lee, T. D., Nucl. Phys. B202, 89 (1982).
Adler, S., in Lectures on Elementary Particles and Quantum Field Theory, MIT Press, 1970.
Bardeen, W. A. and Zumino, B., Nucl. Phys. B244, 421 (1984).
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Guo, HY., Ren, HC. & Wu, K. Conformal anomaly, virasoro algebra and Chern—Simons cohomology. Lett Math Phys 12, 181–188 (1986). https://doi.org/10.1007/BF00416507
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DOI: https://doi.org/10.1007/BF00416507