There has been recent interest in the question of whether four dimensional scale invariant unitary quantum field theories are actually conformally invariant. In this note we present a complete analysis of possible scale anomalies in correlation functions of the trace of the stress-energy tensor in such theories. We find that 2-, 3- and 4-point functions have a non-trivial anomaly while connected higher point functions are non-anomalous. We pay special attention to semi-local contributions to correlators (terms with support on a set containing both coincident and separated points) and show that the anomalies in 3- and 4-point functions can be accounted for by such contributions. We discuss the implications of the our results for the question of scale versus conformal invariance.
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms, linearized Weyl rescalings, and conformal transformations.
We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conform…
There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + ε$ dimensions, but the naive extension has a small loophole, which indeed shows an obstruction in non-linear sigma models in $2+ε$ dimensions. Even though it could have failed due to the loophole, we show that scale invariance does imply conformal invariance of non-linear sigma models in $2+ε$ dimension from the seminal work by Perelman on the Ricci flow.
Implications are explored of promoting non-conformal scale-invariant theories to conformal theories by nonlinearly realizing the missing symmetry. Properties of the associated Nambu-Goldstone mode imply that conformal invariance cannot be spontaneously broken to scale invariance in unitary theories and that, as well known, scale invariant unitary theories in two dimensions are also conformal. The promoted theories have only conformal primaries and no descendants. The (non-)decoupling of the Nambu-Goldstone mode is explicitly shown in examples of scale invariant theories that are actually (not)…
I will discuss spontaneous conformal symmetry breaking in the strongly $γ$-deformed limit of the $\mathcal N=4$ supersymmetric Yang-Mills theory known as~\emph{Fishnet Conformal Field Theory}.
利用精确重整化群的形式，讨论了Wilson作用量的共形不变性的实现。这一问题在O. J. Rosten本文的主要目的是重新制定Rosten公式的共形变换使用的方法开发较早的实现任何连续对称的精确重整化群形式主义。重新表述的优点是简单和透明，通过一致使用的运动方程运营商。我们推导出方程，这意味着不变性的威尔逊行动下的无穷小的共形变换是非线性实现的，但形成一个封闭的共形代数。已尽最大努力，使文件自成一体的形式主义提供了充足的背景。
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions. That is because conformal field theories form a large class of massless no-scale renormalizable quantum field theories. It is generally believed, however, that renormalization breaks conformal invariance and with the absence of a reported success to find a conformally invariant renormalization scheme, an alternative approach is followed in this thesis. We beg…
