重新诠释超对称

中文摘要 AI 辅助

数学上优雅且极具潜力的超对称理念正面临严峻挑战，因为其常规弱能标实现方式正因超对称伴子缺乏实验证据而受到日益严格的约束。然而，我们指出，预言新的（看似不存在的）超对称粒子并非必要：若我们略微放宽对超对称模型的预期，N扩展超对称的生成元$Q^a_\beta$可被轻易诠释为带有内部规范群的量子数，从而将具有不同规范属性的粒子联系起来。在这一视角下，算符$Q^a_\beta$仍是平移的“平方根”，但本身并不生成模型的对称性，它们仅代表在数学上联系玻色场与费米场的变换；仅形如$\textstyle\bigoplus_a \big{[}Q^a_\beta, \bar{Q}_{a\beta}\big{]}$的规范不变组合对应时空动量，因而代表模型的对称性。通过这一概念修正，最简杨-米尔斯超对称模型不再将矢量玻色子与假设的规范微子联系，而是与远非奇特的手征费米子（例如左手轻子）联系；进一步添加一个Higgs标量的SU(2)二重态不再引入Higgsino，而是一个自然对应右手轻子的费米子，且熟悉的Yukawa项作为数学必然性出现。尽管放弃了算符$Q^a_\beta$单独生成作用量对称性的要求，这一超对称方法在数学上与标准SUSY极为相似，有望保留标准超对称的诸多优良性质，同时潜在地使超对称理念与实验数据相协调。该方法仍具有相当的约束性：此类模型的相对系数被严格确定。

英文摘要

The mathematically elegant and promising idea of supersymmetry faces severe challenges as its conventional weak-scale realizations are increasingly constrained by the lack of experimental evidence of superpartners. However, we point out that the prediction of new (seemingly non-existing) supersymmetric particles is not a necessity: if we slightly relax our expectations from the supersymmetric models, generators $Q^a_α$ of $N$-extended supersymmetry can be readily interpreted as carrying a quantum number of the internal gauge group, thus connecting particles with different gauge properties. In this view, operators $Q^a_α$ remain ``square roots'' of translations, but do not by themselves generate symmetries of the model. They merely represent transformations that mathematically relate bosonic and fermionic fields; it is only the gauge-invariant combinations of the form $\sum_a \{Q^a_α, \bar Q_{aβ}\}$ that correspond to spacetime momenta and thus represent symmetries of the model. With this conceptual modification, the simplest Yang-Mills supersymmetric model no longer connects vector bosons with hypothetical gauginos, but with far less exotic chiral fermions, e.g.\ with left-handed leptons. Further adding an $SU(2)$ doublet of Higgs scalars no longer introduces Higgsinos, but a fermion that naturally corresponds to the right-handed lepton, with the familiar Yukawa term showing up as a mathematical necessity. Despite giving up the requirement that operators $Q^a_α$ alone generate symmetries of the action, this approach to supersymmetry is strikingly mathematically similar to standard SUSY, raising hopes that many of the favorable properties of standard supersymmetry can be retained, while potentially reconciling the idea of supersymmetry with experimental data. The approach is still quite restrictive: the relative coefficients of such models are strongly determined.

发表机构

• Institute of Physics, Belgrade University（贝尔格莱德大学物理研究所）

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