Euclidean actions, instantons, solitons and supersymmetry
Euclidean actions, instantons, solitons and supersymmetry
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欧几里得作用、瞬子、孤子和超对称性
DOI：
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发表时间：
2010
期刊：
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通讯作者：
K. Waite
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文献类型：
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作者：
T. Mohaupt;K. Waite
轴子标量理论允许三种不同的欧几里德公式，分别是Wick旋转、Wick旋转结合轴标量的解析延拓和Wick旋转结合Hodge对偶得到的。我们研究了一类包含N=2向量乘子的Sigma模型作为特例的理论的这些公式之间的关系。结果表明，半经典振幅可以用这两种轴子作用量等价地表示，而Hodge对偶化形式给出了不同的瞬子作用量，除非以特定的方式选择与轴子场有关的积分常数。在这种情况下，瞬子作用量等于孤子或黑洞的质量，这是通过对时间的维度提升而获得的。对于超对称模型，我们利用欧几里德超对称代数导出了欧氏BPS条件，并给出了区分BPS极解和非BPS极解的几何准则。
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 identify a geometrical criterion which distinguishes BPS from non-BPS extremal solutions.