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Anomalies and superspace constraints in Green-Schwarz heterotic string. (English) Zbl 0678.53083
Geometrical and algebraic aspects of nonlinear field theory, Proc. Meet., Amalfi/Italy 1988, 229-248 (1989).
[For the entire collection see Zbl 0667.00020.]
The author first reviews the superspace formulation of $$N=1$$, $$D=10$$ supergravity-super Yang Mills models, including the anomaly free models based on the Green-Schwarz mechanism [M. B. Green and J. H. Schwarz, Nucl. Phys. B 243, 285-306 (1984)]. He then considers the manifestly spacetime supersymmetric Green-Schwarz formulation [M. B. Green and J. H. Schwarz, ibid. 255, 93-114 (1985)] of the heterotic string [P. J. Gross, J. A. Harvey, E. Martinec and R. Rohm, ibid. 256, 253-284 (1985)] in a Yang-Mills and a curved superspace background. Despite the well-known difficulties with quantization in this formulation he derives the general structure of the anomaly associated with Siegel’s fermionic $$\kappa$$-symmetry [W. Siegel, Phys. Lett. B 128, 397-399 (1983)] and of the conformal anomaly. The consistency conditions for the $$\kappa$$-anomalies are found to agree with the superspace constraints of the supergravity-super Yang Mills models, and it is argued that the conformal anomalies vanish once the $$\kappa$$-anomalies are cancelled.
Reviewer: H.Rumpf

##### MSC:
 53C80 Applications of global differential geometry to the sciences 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory