arXiv 2206.097052022-06hep-thhep-ph

四维伴随多标量规范理论的单圈不动点

One-loop fixed points of adjoint multi-scalar gauge theory in four dimensions

Nadia Flodgren, Bo Sundborg

备注：: The preprint is withrawn because of its erroneous conclusion on real fixed points. The determination of coefficients in equation 6.1 was mistaken, not to the algebraic approach, and correct results will be published in a different context

摘要：

本文确定了四维$SU(N)$规范理论中多标量四点耦合的完整单圈β函数。对于伴随标量，单圈规范耦合β函数的符号仅依赖于$M$，在$M=22$处消失并改变符号。对于固定规范耦合下的多标量势，我们在大$N$中找到了几个具有不同稳定性的不动点。分析关键涉及四个$SU(N)$和$O(M)$不变的单迹和双迹耦合的全套。在考虑规范耦合的情况下，$M<22$存在渐近自由的RG流，$M=22$在一个环上存在非平凡的不动点，而$M>22$破坏了理论的UV性质.令人惊讶的是，在$M=22$和$M=21$之间，固定流的数量在大$N$限制中从8个下降到4个。$M=22$似乎有一些非常特别的东西。更推测地，$M=22$单圈共形不动点理论与$M$伴随标量在$d=4$建议一个孤立的非超对称，纯玻色子AdS $_{4+1} \times$ S $^{22-1}$ /CFT $_4$对应的可能性。我们的例子表明，将势扩展到对称性所允许的完整项集可能会导致实不动点，这也适用于从$\mathcal{N}=4$ super-Yang-Mills理论发展而来的非超对称理论。

英文摘要：

We determine complete one-loop beta functions of the multi-scalar four-point couplings in four-dimensional $SU(N)$ gauge theories with $M$ adjoint scalar multiplets. For adjoints scalars, the sign of the one loop gauge coupling beta function depends solely on $M$, vanishing and changing sign precisely at $M=22$. For the multi-scalar potential at fixed gauge coupling we find several fixed points with different stability properties at large $N$. The analysis crucially involves the full set of four $SU(N)$ and $O(M)$ invariant single trace and double trace couplings. Taking the gauge coupling into account, there are asymptotically free RG flows for $M<22$ and non-trivial fixed points for $M=22$ at one loop, while $M>22$ appears to ruin the UV properties of the theory. Surprisingly, uniquely between $M=22$ and $M=21$ the number of fixed flows drops from eight to four in the large $N$ limit. There seems to be something very special about $M=22$. More speculatively, the $M=22$ one-loop conformal fixed point theory with $M$ adjoint scalars in $d=4$ suggests the possibility of an isolated non-supersymmetric, purely bosonic AdS$_{4+1} \times$S$^{22-1}$/CFT$_4$ correspondence. Our example suggests that extending the potential to the complete set of terms allowed by symmetries may lead to real fixed points also in non-supersymmetric theories descending from $\mathcal{N}=4$ super-Yang-Mills theory.

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