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arXiv 1507.04424hep-th
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偶然对称与共形引导

Accidental Symmetries and the Conformal Bootstrap

Shai M. Chester, Simone Giombi, Luca V. Iliesiu, Igor R. Klebanov, Silviu S. Pufu, Ran Yacoby

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26 pages, 5 figures
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摘要：

本文研究了三维临界$O(N)$矢量模型的${\cal N} = 2$超对称推广，该模型由具有超势$W = g_1 X \sum_i Z_i^2 + g_2 X^3$的$N+1$手征超场描述。通过将共形引导工具与超对称局部化结果相结合，我们认为该模型在红外超共形不动点处由于$g_2$流到零而表现出对称性增强.这个例子的特殊之处在于，具有$g_1,g_2\neq 0$的红外固定点的存在，其不表现出对称性增强，通常不会导致任何明显的么正性违反或其他不一致。然而，我们证明了$F$定理排除了具有$g_1,g_2\neq 0$的模型对于$N>5$。共形引导提供了更强的约束，并排除了$N>2$的此类模型。我们提供的证据表明，$g_2=0$模型，它具有增强的$O(N)\times U(1)$对称性，接近饱和的自举边界。我们将我们的分析扩展到分数维，在那里我们可以激励不存在的$g_1,g_2\neq 0$模型，通过研究他们的$4-ε$扩展微扰。

英文摘要：

We study an ${\cal N} = 2$ supersymmetric generalization of the three-dimensional critical $O(N)$ vector model that is described by $N+1$ chiral superfields with superpotential $W = g_1 X \sum_i Z_i^2 + g_2 X^3$. By combining the tools of the conformal bootstrap with results obtained through supersymmetric localization, we argue that this model exhibits a symmetry enhancement at the infrared superconformal fixed point due to $g_2$ flowing to zero. This example is special in that the existence of an infrared fixed point with $g_1,g_2\neq 0$, which does not exhibit symmetry enhancement, does not generally lead to any obvious unitarity violations or other inconsistencies. We do show, however, that the $F$-theorem excludes the models with $g_1,g_2\neq 0$ for $N>5$. The conformal bootstrap provides a stronger constraint and excludes such models for $N>2$. We provide evidence that the $g_2=0$ models, which have the enhanced $O(N)\times U(1)$ symmetry, come close to saturating the bootstrap bounds. We extend our analysis to fractional dimensions where we can motivate the nonexistence of the $g_1,g_2\neq 0$ models by studying them perturbatively in the $4-ε$ expansion.

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