arXiv math-ph/02050472002-05math-phhep-thmath.ATmath.MP

关于任意李代数Wess-Zumino相容性条件的结果

Results on the Wess-Zumino consistency condition for arbitrary Lie algebras

A. Barkallil, G. Barnich, C. Schomblond

备注：: 39 pages Latex file, 1 eps figure, typos and proof of lemma 5 corrected
发表信息：: J.Math.Phys. 43 (2002) 5987-6015
DOI：: 10.1063/1.1513209

摘要：

将BRST微分的规范部分的上同调中时空外导数的诱导上同调的所谓协变Poincare引理推广到任意非约化李代数的情形.因此，Wess-Zumino相容性条件的非平凡下降的一般解决方案，可以为任意的（超）李代数，计算在小代数的1形式的潜力，鬼和他们的外部衍生物。对于特定的李代数是半单李子代数与理想的半直和，一个定理由Hochschild和塞尔是用来更精确地刻画的规范部分的上同调的BRST微分在小代数。在阿贝尔理想的情况下，这导致了Wess-Zumino相容性条件在这个空间中的完全解。作为应用，重新讨论了基于iso（2，1）的2+1维Chern-Simons理论的相容变形.

英文摘要：

The so-called covariant Poincare lemma on the induced cohomology of the spacetime exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, non reductive Lie algebras. As a consequence, the general solution of the Wess-Zumino consistency condition with a non trivial descent can, for arbitrary (super) Lie algebras, be computed in the small algebra of the 1 form potentials, the ghosts and their exterior derivatives. For particular Lie algebras that are the semidirect sum of a semisimple Lie subalgebra with an ideal, a theorem by Hochschild and Serre is used to characterize more precisely the cohomology of the gauge part of the BRST differential in the small algebra. In the case of an abelian ideal, this leads to a complete solution of the Wess-Zumino consistency condition in this space. As an application, the consistent deformations of 2+1 dimensional Chern-Simons theory based on iso(2,1) are rediscussed.

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