For certain terms in the action, supersymmetry can forbid an infinite number of possible contributions. We study whether such protection can occur in quantum gravity even without sufficient supersymmetry. We focus on whether the superpotential can vanish exactly in four-dimensional N $$ \mathcal{N} $$ = 1 theories, and if the prepotential can be exactly cubic in N $$ \mathcal{N} $$ = 2 theories. We investigate these questions in string theory and find that for almost all known string constructions the corrections allowed by supersymmetry do occur. However, we do find some special settings where all the corrections can be proven to vanish. These examples all share the common feature that they are related, through a certain orbifolding by a discrete gauged R-symmetry element, to a higher supersymmetric theory. Motivated by these results, we propose a Swampland criterion that any theory which enjoys such protection beyond its realised supersymmetry must have a direct connection to a higher supersymmetric theory.

中文翻译：

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超对称保护和沼泽地

对于动作中的某些项，超对称性可以禁止无限数量的可能贡献。我们研究了即使没有足够的超对称性，这种保护是否也能在量子引力中发生。我们关注超势是否可以在四维 N $$ \mathcal{N} $$ = 1 理论中完全消失，以及在 N $$ \mathcal{N} $$ = 2 理论中超势是否可以精确为三次。我们在弦理论中研究了这些问题，并发现对于几乎所有已知的弦结构，超对称所允许​​的修正确实发生了。但是，我们确实找到了一些特殊设置，可以证明所有更正都消失了。这些例子都有一个共同的特征，即它们通过离散规范 R 对称元素的某种轨道折叠与更高的超对称理论相关。受这些结果的鼓舞，