The supersymmetric Lee–Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit nonunitary. A natural question is if there is an analogue of supersymmetric Lee–Yang fixed point in higher dimensions. The absence of any ℤ2 symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative 𝜖 expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supersymmetric Lee–Yang fixed point in three dimensions. We conjecture that the corresponding phase transition, if any, will be the first-order transition.

中文翻译：

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三维空间中是否存在超对称李阳不动点？

超对称 Lee-Yang 模型可以说是二维中最简单的相互作用超对称场论，尽管它是非统一的。一个自然的问题是在高维中是否存在超对称李杨不动点的类似物。没有任何ℤ2对称性（费米子数除外）使得不可能通过使用微扰来接近它𝜖扩展。我们发现截断的保形自举表明，通过二维的维度延续获得的候选不动点在三个维度以下湮灭，这意味着在三个维度上不存在超对称的 Lee-Yang 不动点。我们推测相应的相变，如果有的话，将是一阶转变。