After a brief outline of general aspects of conformal field theories in coordinate space, in a first part we review the solution of the conformal constraints of three- and four-point functions in momentum space in dimensions $d\geq 2$, in the form of conformal Ward identities (CWI's). We center our discussion on the analysis of correlators containing stress-energy tensors $(T)$, conserved currents $(J)$, and scalar operators $(O)$. For scalar four-point functions, we briefly discuss our method for determining the dual conformal solutions of such equations, identified only by the CWI's, and related to the conformal Yangian symmetry, introduced by us in previous work. In correlation functions with $T$ tensors, evaluated around a flat spacetime, the conformal anomaly is characterized by the (non-local) exchange of massless poles in specific form factors, a signature that has been investigated both in free field theory and non-perturbatively, by solving the conformal constraints. We discuss the anomaly effective action, and illustrate the derivation of the CWI's directly from its path integral definition and its Weyl symmetry, which is alternative to the standard operatorial approach used in conformal field theories in flat space. For two- and three-point functions, we elaborate on the matching of these types of correlators to free-field theories. Perturbative realizations of CFTs at one-loop provide the simplest expressions of the general solutions identified by the CWI's, for generic operators $T$, $J$, and scalars of specific scaling dimensions, by an appropriate choice of their field content. In a technical appendix we offer details on the reconstruction of the $TTO$ and $TTT$ correlators in the approach of Bzowski, McFadden and Skenderis, and specifically on the secondary Ward identities of the method, in order to establish a complete match with the perturbative description.
We give a general definition of the conformal anomaly for theories that are not classically Weyl invariant and show that this definition yields a quantity that is both finite and local. As an example we study the conformal anomaly for a non-minimally coupled massless scalar and show that our definition coincides with results obtained using the heat kernel method.
Conformal Anomaly for Dilaton Coupled Theories from AdS/CFT Correspondence
利用AdS/CFT对应，从超重力的角度，发现了在非零的弯曲背景下，作为红外效应的耦合共形理论的迹线异常。对于$d=2$，它与膨胀子耦合标量的共形异常（直到已知不明确的总导数项）相一致。在四维情形下，我们得到了${\cal N}=4$ super YM理论与共形超引力相互作用的共形反常。同样地，在更高的维度中，与声子相关的共形反常的计算似乎比使用标准QFT方法容易得多。
We study the conformal properties of pseudo-scalar (parity-odd) operators in four-dimensional field theory. Such operators include the topological term in a gauge theory and the Yukawa coupling. We show that a single operator of this type cannot be a conformal primary on its own. This is only possible for certain mixtures of pseudo-scalar operators like the chiral Lagrangian of ${\cal N}=4$ super-Yang-Mills theory. We examine the detailed mechanism of conformal symmetry breakdown and derive an anomalous conformal Ward identity. We explore a possible link between this conformal anomaly and the …
We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, ma…
We rederive the conformal anomaly for spin-1/2 fermions by a genuine Feynman graph calculation, which has not been available so far. Although our calculation merely confirms a result that has been known for a long time, the derivation is new, and thus furnishes a method to investigate more complicated cases (in particular concerning the significance of the quantum trace of the stress tensor in non-conformal theories) where there remain several outstanding and unresolved issues.
Trace Anomaly and Non-Local Effective Action for 2D Conformally Invariant Scalar Interacting with Dilaton
利用单回路有效作用的计算结果（E。Elizalde et al，Phys.Rev. D49（1994）2852），我们发现了大多数共形不变的二维标量-标量耦合系统的迹反常（包括了标量-标量耦合系统中标量子本身的贡献）。发现了这类系统的共形反常诱导的非定域有效作用量，为推广类CGHS模型研究物质对二维黑洞的反作用提供了新的可能性。
We consider Polyakov theory of Bosonic strings in conformal gauge which are used to study conformal anomaly. However it exhibits ghost number anomaly. We show how this anomaly can be avoided by connecting this theory to that of in background covariant harmonic gauge which is known to be free from conformal and ghost number current anomaly, by using suitably constructed finite field dependent BRST transformation.
Conformal a-anomaly of some non-unitary 6d superconformal theories
本文计算了某些非幺正（高阶导数或非规范不变）6维共形场及其超多重态的共形反常a系数。我们使用的方法是基于S^6上的6d行列式和AdS_7上的7 d行列式之间的联系。我们特别发现，含有4阶导数规范不变共形矢量的（1，0）超多重态与arXiv：1506.03807（基于R对称性和引力t Hooft匹配）中的标准（1，0）矢量多重态的a反常值完全相同。我们还证明了与26个张量多重态耦合的高阶导数（2，0）6d共形超引力具有消失的a-反常。这是已知的N=4共形超引力耦合到4个矢量N=4多重态的四维系统中共形异常抵消的事实的6d对应物。在5张量多重态被选择为幽灵状并且共形对称性被二次标量约束自发破缺的情况下，所得到的IR理论可以被识别为与21=26-5张量多重态耦合的（2，0）庞加莱超引力。后一种理论被认为是特殊的：它是无重力异常的，并且是K3上10 d IIB型超重力紧化的结果。
In previous work, we showed that an anomaly in the one point function of marginal operators is related by the Wess-Zumino condition to the Euler density anomaly on a two dimensional defect or boundary. Here we analyze in detail the two point functions of marginal operators with the stress tensor and with the displacement operator in three dimensions. We show how to get the boundary anomaly from these bulk two point functions and find perfect agreement with our anomaly effective action. For a higher dimensional conformal field theory with a four dimensional defect, we describe for the first tim…
We propose general relations between the conformal anomaly and the chiral (R-symmetry and gravitational) anomaly coefficients in 6d (1,0) superconformal theories. The suggested expressions for the three type B conformal anomaly c-coefficients complement the expression for the type A anomaly a-coefficient found in arXiv:1506.03807. We check them on several examples -- the standard (1,0) hyper and tensor multiplets as well as some higher derivative short multiplets containing vector fields that generalize the superconformal 6d vector multiplet discussed in arXiv:1506.08727. We also consider a fa…
We consider conformal and 't Hooft anomalies in six-dimensional ${\cal N}=(1,0)$ superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and $SU(2)_R$ currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non-supersymmetric CFTs in six dimensions have three independent conformal $c$-anomalies, which determine the stress-tensor two- and three-point functions, but in superc…
The conformal anomaly is computed on even $d$--spheres for a $p$--form propagating according to the Branson--Gover higher derivative, conformally covariant operators. The system is set up on a $q$--deformed sphere and the conformal anomaly is computed as a rational function of the derivative order, $2k$, and of $q$. The anomaly is shown to be an extremum at the round sphere ($q=1$) only for $k<d/2$. At these integer values, therefore, the entanglement entropy is minus the conformal anomaly, as usual. The unconstrained $p$--form conformal anomaly on the full sphere is shown to be given by an in…
We elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations $(h)$ of the background metric, in the flat spacetime limit. For this purpose we discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions with the goal of identifying the structure of the anomaly action. We focus on a separation of the correlator into its transverse/traceless and longitudinal components, applied to the trace and conservation Ward identitie…
