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arXiv 1508.02481hep-th
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超弦微扰理论中的超对称性恢复

Supersymmetry Restoration in Superstring Perturbation Theory

Ashoke Sen

摘要:

基于1 PI有效理论方法的超弦微扰理论对于解决质量重整化和真空位移问题是有用的。在这种方法中,我们导出了与时空超对称变换相关的沃德恒等式。这导致了一个证明的重整化质量的玻色子和费米子和身份有关的费米子振幅玻色子振幅后,考虑到质量重整化的影响。这也将未破缺的超对称性与微扰论中给定的阶数联系起来,与无质量标量的蝌蚪的缺乏联系起来。当位移真空描述了理论的正确基态时,结果在微扰真空和位移真空中都有效。我们将此应用于卡-丘3-折叠上的SO(32)杂化弦论,其中一个圈的Fayet-Iliopoulos项显然在一个圈处破坏了超对称性,但对低能有效场论的分析表明,在附近有一个真空,超对称性在那里恢复。我们明确地证明了这个理论在移动真空附近的微扰振幅确实满足与未破缺超对称性有关的沃德恒等式。我们还测试的一般参数,明确验证玻色子和费米子质量的平等,在一个循环的顺序在移动的真空中,和外观的两个循环的蝌蚪在微扰真空中的超对称性预计将被打破。

英文摘要:

Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.

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