Related papers: Generalization of conformal Hamada operators
Conformal properties of the topological gravitational terms in $D=2$, $D=4$ and $D=6$ are discussed. It is shown that in the last two cases the integrands of these terms, when being settled into the dimension $D-1$ and multiplied by a…
We continue the study of model-independent constraints on the unitary Conformal Field Theories in 4-Dimensions, initiated in arXiv:0807.0004. Our main result is an improved upper bound on the dimension \Delta of the leading scalar operator…
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions $d$. Calculations of the universal function of a conformal invariant $\xi$ which appears in…
It was demonstrated in recent work that $d=4$ unitary CFT's satisfy a special property: if a scalar operator with conformal dimension $\Delta$ exists in the operator spectrum, then the conformal bootstrap demands that large spin primary…
Using (2+$\epsilon$)-dimensional quantum gravity recently formulated by Kawai, Kitazawa and Ninomiya, we calculate the scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity coupled to $(p,q)$…
Total derivative terms play an important role in the integration of conformal anomaly. In four dimensional space $4D$ there is only one such term, namely $\,{\square}R$. In the case of six dimensions $6D$ the structure of surface terms is…
We perform a comprehensive perturbative study of the operator spectrum in multi-scalar theories with hypercubic global symmetry. This includes working out symmetry representations and their corresponding tensor structures. These structures…
We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an…
Conformal blocks play a central role in CFTs as the basic, theory-independent building blocks. However, only limited results are available concerning multipoint blocks associated with the global conformal group. In this paper, we…
We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal…
We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We…
Curved algebras are a generalization of differential graded algebras which have found numerous applications recently. The goal of this foundational article is to introduce the notion of a curved operad, and to develop the operadic calculus…
The conventional model of the gauge vector field is invariant under the local conformal symmetry only in the four-dimensional space ($4d$). Conformal generalization to an arbitrary dimension $d$ is impossible even for the free theory,…
In this letter we discuss the operator product expansion of scalar operators in five-dimensional field theories with an $SU(1,3)\times U(1)$ spacetime symmetry. Such theories arise by a novel conformal null reduction of six-dimensional…
We discuss the general covariance of operator product expansion in D-dimensional Euclidean conformal field theories. We propose to organise the expansion in powers of geodesic distance between two insertion points and to use the tangent…
We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the…
The n-point functions of any Conformal Field Theory (CFT) in $d$ dimensions can always be interpreted as spatial restrictions of corresponding functions in a higher-dimensional CFT with dimension $d'> d$. In particular, when a four-point…
Given a complex manifold $X$ and a smooth positive function $\eta$ thereon, we perturb the standard differential operator $d=\partial + \bar\partial$ acting on differential forms to a first-order differential operator $D_\eta$ whose…
We compute $d$-dimensional scalar six-point conformal blocks in the two possible topologies allowed by the operator product expansion. Our computation is a simple application of the embedding space operator product expansion formalism…
We calculate the order \lambda, \lambda^2 and \lambda y^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where \lambda and y are the Standard Model Higgs self-coupling and a generic Yukawa coupling,…