arXiv 0907.11012009-07-14hep-thastro-ph.COcond-mat.supr-conhep-phmath.AT

任意D中的Dirac膜和反常项/Chern-Simons项

Dirac Branes and Anomalies/Chern-Simons terms in any D

Christopher T. Hill

备注：: 24 pages, 7 figures; v2 fixes some typographical and sign errors

摘要：

利用狄拉克量子化方法，通过自洽论证，可以导出D=3的Chern-Simons项的系数，并可以推广到任意奇数D。这就产生了D-1边界上的一致和协变的轴向异常系数，以及D中的Chern-Simons项系数。在D=3磁单极子不存在，如果陈-西蒙斯AdA项是存在的。于是狄拉克螺线管就变成了一个携带电流的物理闭合弦。弦上的载流子必须与狄拉克螺线管通量的电荷一致。这就产生了陈-西蒙斯项系数。在更高的奇数D中，（D-1）/2狄拉克膜的相交产生了一个允许相容性论证的带电世界线。协变异常系数很容易从推广的反项。这种纯粹的玻色子推导异常是相当简单的，涉及精确积分的半经典评估，如\int dAdA. dA，在膜的交叉处。

英文摘要：

The Dirac quantization procedure of a magnetic monopole can be used to derive the coefficient of the D=3 Chern-Simons term through a self-consistency argument, which can be readily generalized to any odd D. This yields consistent and covariant axial anomaly coefficients on a D-1 boundary, and Chern-Simons term coefficients in D. In D=3 magnetic monopoles cannot exist if the Chern-Simons AdA term is present. The Dirac solenoid then becomes a physical closed string carrying electric current. The charge carriers on the string must be consistent with the charge used to quantize the Dirac solenoidal flux. This yields the Chern-Simons term coefficient. In higher odd D the intersection of (D-1)/2 Dirac branes yields a charged world-line permitting the consistency argument. The covariant anomaly coefficients follow readily from generalizing the counterterm. This purely bosonic derivation of anomalies is quite simple, involving semiclassical evaluation of exact integrals, like \int dAdA...dA, in the brane intersections.

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摘要：

英文摘要：

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