论文标题
在四个维
One-loop fixed points of adjoint multi-scalar gauge theory in four dimensions
论文作者
论文摘要
我们确定具有$ M $ a $ apecoint capeind scalar多重组的四维$ su（n）$仪表理论的多尺度四点耦合的完整一环beta函数。对于伴随标量，一个环路耦合β函数的符号仅取决于$ m $，消失和更改标志正好在$ m = 22 $。对于固定量规耦合处的多量表电位，我们找到了几个固定点，其稳定性属性在$ n $上都具有不同的稳定性。该分析至关重要涉及四个$ su（n）$和$ o（m）$不变的单个跟踪和双重跟踪耦合的完整组。考虑到量规耦合，在一个循环时以$ m <22美元的价格出现渐近免费的RG流，$ m = 22 $，而非平凡的固定点，而$ m> 22美元似乎会破坏该理论的UV属性。令人惊讶的是，在$ n $限制中，固定流量的数量从八个下降到四个。大约$ m = 22美元似乎有一些非常特别的东西。更猜测，$ M = 22 $一环固定点理论，$ m $ axpaint callars in $ d = 4 $表明有可能出现孤立的非苏绝端的，纯粹的骨质ADS $ _ {4+1} \ times $ s $ s $ s $ s $^{22-1} $^{22-1} $/cft $ _4 $ _4 $。 我们的示例表明，将潜力扩展到对称性允许的完整术语集可能会导致实际固定点，从$ \ Mathcal {n} = 4 $ super-yang-mills理论中降低的非苏绝端理论中。
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.
