Low-energy theorem and OPE in the conformal window of massless QCD
Marco Bochicchio, Elisabetta Pallante
备注：
91 pages, no figures. We have replaced the conformal ansatz in the former eq. (7.3) with the ansatz for the exact solution of the Callan-Symanzik equation and extensively rewritten the paper
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.
A First-Quantized Model For Unparticles and Gauge Theories Around Conformal Window
我们首先验证了Casalbuoni和Gomis在[Phys. Rev. D \textbf{90}，026001（2014）]中提出的作用量，该作用量描述了两个无质量相对论标量粒子通过共形不变势相互作用。光谱是可以解释为非粒子的质量态的连续体。然后，我们以类似的方式获得了变形作用量的质量算符，其中引入了两个破坏共形对称性的项：质量项和额外的依赖于位置的耦合常数。对后者作一个简单的分析，就得到一个以有效弦张力$σ\,$表示的具有线性约束的质量算符。当$σ\neq0$及其质谱呈现Regge轨道时，量子化模型是有局限性的.我们提出了一个无张力的限制，其中高度激发的限制态减少（带隙）unparticles。此外，在后一个极限中，作为共形对称恢复的标志，低位受限束缚态变得无质量，并且它们的质量与$\sqrtσ$之间的比率保持恒定。我们的方法的独创性是，它适用于限制和共形阶段通过一个有效的相互作用模型。
Revisiting Schrödinger CFTs: Factorization, Massless Particles, and a Path to the Bootstrap
Yang Institute for Theoretical Physics, Stony Brook University（杨理论物理研究所，石溪大学）；Simons Center for Geometry and Physics, Stony Brook University（西蒙斯几何与物理中心，石溪大学）；Department of Physics and Astronomy, Stony Brook University（物理学与天文学系，石溪大学）
