In a September 1976 PRL Eguchi and Freund considered two topological invariants: the Pontryagin number ##IMG## [http://ej.iop.org/images/1751-8121/53/30/301001/aab956dieqn1.gif] {$P\sim \int {\mathrm{d}}^{4}x\sqrt{g}{R}^{{\ast}}R$} and the Euler number ##IMG## [http://ej.iop.org/images/1751-8121/53/30/301001/aab956dieqn2.gif] {$\chi \sim \int {\mathrm{d}}^{4}x\sqrt{g}{R}^{{\ast}}{R}^{{\ast}}$} and posed the question: to what anomalies do they contribute? They found that P appears in the integrated divergence of the axial fermion number current, thus providing a novel topological interpretation of the anomaly found by Kimura in 1969 and Delbourgo and Salam in 1972. However, they found no analogous role for χ . This provoked my interest and, drawing on my April 1976 paper with Deser and Isham on gravitational Weyl anomalies, I was able to show that for conformal field theories the trace of the stress tensor depends on just t...

中文翻译：

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魏尔，蓬特里亚金，欧拉，江口和弗洛因德

1976年9月，PRL Eguchi和Freund考虑了两个拓扑不变式：Pontryagin编号## IMG ## [http://ej.iop.org/images/1751-8121/53/30/301001/aab956dieqn1.gif] {$ P \ sim \ int {\ mathrm {d}} ^ {4} x \ sqrt {g} {R} ^ {{\ ast}} R $}和欧拉数## IMG ## [http：// ej .iop.org / images / 1751-8121 / 53/30/301001 / aab956dieqn2.gif] {$ \ chi \ sim \ int {\ mathrm {d}} ^ {4} x \ sqrt {g} {R} ^ {{\ ast}} {R} ^ {{\ ast}} $}，并提出了一个问题：它们对异常造成了什么影响？他们发现P出现在轴向费米子数电流的积分散度中，从而为Kimura在1969年以及Delbourgo和Salam在1972年发现的异常提供了一种新颖的拓扑解释。但是，他们没有发现χ的类似作用。这激起了我的兴趣，并根据我与Deser和Isham于1976年4月发表的关于重力Weyl异常的论文，