Related papers: Conformal $n$-point functions in momentum space
Conformal blocks for four point functions for fields with arbitrary spins in two dimensions are obtained by evaluating an appropriate integral. The results are just products of hypergeometric functions of the conformally invariant cross…
The covariant two-point functions, derived from Ward identities in direct space, can be affected by consistency problems and can become unbounded for large time- or space-separations. This difficulty arises for several extensions of…
A method of functional reduction for the dimensionally regularized one-loop Feynman integrals with massive propagators is described in detail. The method is based on a repeated application of the functional relations proposed by the author.…
In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 SYM theory. In this letter we show that integrability also features in the building blocks of massive…
The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy…
We systematically derive the consistency relations associated to the non-linearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearly-realized de Sitter subalgebra. These identities relate…
We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate (N+1)-point correlation functions with a…
We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a…
Four-dimensional N-extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms…
Further results for conformal partial waves for four point functions for conformal primary scalar fields in conformally invariant theories are obtained. They are defined as eigenfunctions of the differential Casimir operators for the…
We present an analytic study of conformal field theories on the real projective space $\mathbb{RP}^d$, focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions…
Conformal blocks are the building blocks for correlation functions in conformal field theories. The four-point function is the most well-studied case. We consider conformal blocks for $n$-point correlation functions. For conformal field…
Single-field perturbations satisfy an infinite number of consistency relations constraining the squeezed limit of correlation functions at each order in the soft momentum. These can be understood as Ward identities for an infinite set of…
In a conformal field theory, two and three-point functions of scalar operators and conserved currents are completely determined, up to constants, by conformal invariance. The expressions for these correlators in Euclidean signature are long…
We review the emergence of hypergeometric structures (of $F_4$ Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions $d > 2$. We illustrate the case of scalar 3- and 4-point functions.…
The requirements of conformal invariance for the two point function of the energy momentum tensor in the neighbourhood of a plane boundary are investigated, restricting the conformal group to those transformations leaving the boundary…
Recently, Bern et al observed that a certain class of next-to-planar Feynman integrals possess a bonus symmetry that is closely related to dual conformal symmetry. It corresponds to a projection of the latter along a certain lightlike…
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality $\langle T^{00} \rangle \ge -C/L^4$, where $L$ is the size of the smearing region, and $C$ is a positive constant that depends on the…
We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of $CFT_d$ four point functions and expands them in terms of crossing symmetric combinations of $AdS_{d+1}$ Witten exchange functions.…
We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations…