In supersymmetric extensions of the Standard Model, the observed particles come in fermion–boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles, not a single supersymmetric pair has been reported to date. Although a hypothetical SUSY breaking mechanism, operating at high energy inaccessible to current experiments cannot be ruled out, this reduces SUSY’s predictive power and it is unclear whether SUSY, in its standard form, can help reducing the remaining puzzles of the standard model (SM). Here we argue that SUSY can be realized in a different way, connecting spacetime and internal bosonic symmetries, combining bosonic gauge fields and fermionic matter particles in a single gauge field, a Lie superalgebra-valued connection. In this unconventional representation, states do not come in SUSY pairs, avoiding the doubling of particles and fields and SUSY is not a fully off-shell invariance of the action. The resulting systems are remarkably simple, closely resembling a standard quantum field theory and SUSY still emerges as a contingent symmetry that depends on the features of the vacuum/ground state. We illustrate the general construction with two examples: (i) A 2 + 1 dimensional system based on the $osp(2,2|2)$ superalgebra, including Lorentz and $u\left(1\right)$ generators that describe graphene; (ii) a supersymmetric extension of 3 + 1 conformal gravity with an $SU(2,2|2)$ connection that describes a gauge theory with an emergent chiral symmetry breaking, coupled to gravity. The extensions to higher odd and even dimensions, as well as the extensions to accommodate more general internal symmetries are also outlined.

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非常规SUSY和常规物理：教学法评论

在标准模型的超对称扩展中，观察到的粒子以实现超对称（SUSY）所必需的费米子-玻色子对的形式出现。尽管对所有已知粒子都期望有大量的超级伙伴，但迄今为止，还没有单个超对称对的报道。尽管不能排除假设的SUSY破坏机制，该机制在当前实验无法达到的高能量下运行，但这会降低SUSY的预测能力，并且不清楚SUSY（其标准形式）是否可以帮助减少标准模型（SM）的其余难题。在这里，我们认为SUSY可以以不同的方式实现，将时空和内部的玻色子对称性联系起来，将玻色子规范场和铁离子物质粒子组合在一个规范场中，即李超代数值连接。在这个非常规表示，状态不以SUSY对形式出现，避免了粒子和场的加倍，并且SUSY并不是动作的完全脱壳不变性。生成的系统非常简单，非常类似于标准量子场论，而SUSY仍然是视情况而定的对称性，取决于真空/基态的特征。我们用两个例子来说明一般构造：（i）一个基于2 + 1维系统$Øsp（\mathrm{2个}，\mathrm{2个}|\mathrm{2个}）$ 超级代数，包括Lorentz和 $ü（\mathrm{1个}）$描述石墨烯的生成器；（ii）3 +1个共形引力的超对称延伸，且$\mathrm{小号}ü（\mathrm{2个}，\mathrm{2个}|\mathrm{2个}）$连接描述了规范理论，其中出现了与手性耦合的新兴手性对称性断裂。还概述了对更高的奇数和偶数尺寸的扩展，以及适应更一般内部对称性的扩展。