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arXiv 1011.6301hep-th
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欧几里德作用、瞬子、孤子和超对称

Euclidean Actions, Instantons, Solitons and Supersymmetry

Thomas Mohaupt, Kirk Waite

摘要:

理论与轴标量承认三个不同的欧几里得公式,获得威克旋转,威克旋转结合解析延续的轴标量,威克旋转结合霍奇对偶。我们调查这些配方之间的关系,一类理论,其中包含的西格玛模型的N=2向量多重态作为一个特殊情况。结果表明,半经典振幅可以表示等价使用两种类型的轴子行动,而霍奇对偶版本给出了一个不同的值的瞬子行动,除非与轴子字段的积分常数选择在一个特定的方式。在这种选择下,瞬子作用量等于通过关于时间的维数提升得到的孤子或黑洞的质量。对于超对称模型,我们使用欧几里德超对称代数推导出欧几里德BPS条件,我们确定了一个几何标准,区分BPS从非BPS极值解。

英文摘要:

Theories with axionic scalars admit three different Euclidean formulations, obtained by Wick rotation, Wick rotation combined with analytic continuation of the axionic scalars, and Wick rotation combined with Hodge dualization. We investigate the relation between these formulations for a class of theories which contains the sigma models of N=2 vector multiplets as a special case. It is shown that semi-classical amplitudes can be expressed equivalently using the two types of axionic actions, while the Hodge dualized version gives a different value for the instanton action unless the integration constants associated with the axion fields are chosen in a particular way. With this choice the instanton action is equal to the mass of the soliton or black hole obtained by dimensional lifting with respect to time. For supersymmetric models we use the Euclidean supersymmetry algebra to derive a Euclidean BPS condition, and we identify a geometrical criterion which distinguishes BPS from non-BPS extremal solutions.

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