整体共形不变量的分解Ⅰ：关于Deser和Schwimmer的一个猜想
The decomposition of Global Conformal Invariants I: On a conjecture of Deser and Schwimmer
摘要：
这是第一次在一系列文件中，我们证明了一个猜想的Deser和Schwimmer关于代数结构的"全球conformal- mal不变量”;这些被定义为共形不变积分的几何标量。该猜想断言任何这样的积分的被积函数都可以表示为局部共形不变量、散度和Chern-Gauss-Bonnet被积函数的线性组合。本文建立了一个迭代过程来证明这个分解.然后，我们推导出两种情况中的第一种情况下的迭代步骤，服从于在[6，7，8]中证明的纯代数结果。
英文摘要：
This is the first in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global confor- mal invariants"; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the Chern-Gauss-Bonnet integrand. In this paper we set up an iterative procedure that proves the decom- position. We then derive the iterative step in the first of two cases, subject to a purely algebraic result which is proven in [6, 7, 8].
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