论文标题
在无质量QCD的保形窗口中低能定理和OPE
Low-energy theorem and OPE in the conformal window of massless QCD
论文作者
论文摘要
我们开发了一种新技术，该技术基于Arxiv中得出的NSVZ类型的低能定理（LET）：1701.07833，用于对具有N $ {} _ f $ siless quarks的su（n）qcd进行的非扰动研究，或者是无质量qcd qcd的quark-或更普遍的ccd quark unive pers $ beta $ in Forkication -performine $ beta。 $ g = g（μ）$重新归一化的量规耦合，在红外线（IR）或紫外线（UV）中承认一个孤立的零，$ g _*$。我们指出，LET设置在3点相关器上的约束，涉及$ tr \，f^2 $的插入，其异常尺寸$γ_{f^2} $以及$ g _*$的多式固定运算符的异常尺寸。这些约束与$ g（μ）\ rightarrow g _*$与$μ\ neq 0，+\ \ \ iftty $固定和ir/uv渐近学的确切形式相结合 - 可能与$/UV的渐近学 - 可能或可能与$/UV的IR/UV限制$ conformentions -us/Uv conforment -us/Uv complose/uv cormertion -us/uv complose/uv complation -us/uv complation -us/uv comprant -us/uv complation -us/uv compry $ us/ub corge/us/uv compript。 固定的。在保形的情况下，我们还讨论了如何与$ tr \，f^2 $在ope中的神秘差异接触术语中存在的裸相关词的理由与在arxiv中的扰动理论中发现的本身：1209.1516，arxiv：arxiv：1407.6921 and arxec in ar arxec in arxiv in arxiv in arxiv in arxiv：1601080108010808。具体来说，如果$γ_{f^2} $不会消失，则在$ tr \，f^2 $的2点相关器的rhs中的发散联系项必须匹配 - 我们通过直接计算的实际计算来验证它实际上是由于非trive骨anmalous anomal anomal anomalous nomal anomal symalous nomal osalous of trivergence of trivial anomalous anomalous trive nomalous nomal os trive trivergence。因此，值得注意的是，由于LET与LHS中的多重重新归一化化，由于RHS中的不同接触项引起的加性重新归一化，以使得LET的适当重新归一化的版本对添加剂的重态化没有任何歧义。
We develop a new technique, based on a low-energy theorem (LET) of NSVZ type derived in arXiv:1701.07833, for the nonperturbative investigation of SU(N) QCD with N${}_f$ massless quarks - or, more generally, of massless QCD-like theories - in phases where the beta function, $β(g)$, with $g=g(μ)$ the renormalized gauge coupling, admits an isolated zero, $g_*$, in the infrared (IR) or ultraviolet (UV). We point out that the LET sets constraints on 3-point correlators involving the insertion of $Tr\, F^2$, its anomalous dimension $γ_{F^2}$, and the anomalous dimensions of multiplicatively renormalizable operators at $g_*$. These constraints intertwine with the exact conformal scaling for $g(μ)\rightarrow g_*$ with $μ\neq 0,+\infty$ fixed and the IR/UV asymptotics - which may or may not coincide with the IR/UV limit of the aforementioned conformal scaling - for $Λ_{\scriptscriptstyle{IR/UV}}$ fixed. In the conformal case we also discuss how the LET for bare correlators is the rationale for the existence in massless QCD of the mysterious divergent contact term in the OPE of $Tr\,F^2$ with itself discovered in perturbation theory in arXiv:1209.1516, arXiv:1407.6921 and computed to all orders in arXiv:1601.08094. Specifically, if $γ_{F^2}$ does not vanish, the divergent contact term in the rhs of the LET for the 2-point correlator of $Tr\,F^2$ has to match - and we verify by direct computation that it actually does - the divergence in the lhs due to the nontrivial anomalous dimension of $Tr\,F^2$. Hence, remarkably, the additive renormalization due to the divergent contact term in the rhs is related by the LET to the multiplicative renormalization in the lhs, in such a way that a suitably renormalized version of the LET has no ambiguity for additive renormalization.
