Related papers: Counting Conformal Correlators

In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

We describe the use of generalized unitarity for the construction of correlation functions of local gauge-invariant operators in general quantum field theories and illustrate this method with several calculations in N=4 super-Yang-Mills…

In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…

We study correlation functions in topologically twisted $\mathcal{N}=2, d=4$ supersymmetric Yang-Mills theory for gauge groups of rank larger than one on compact four-manifolds $X$. We find that the topological invariance of the generator…

Generalizations of vector field theories to tensors allow to similarly apply large-$N$ techniques but find a richer though often still tractable structure. However, the potential of such tensor theories has not been fully exploited since…

For certain mass values, shift symmetries appear among massive higher spin fields propagating on (anti-) de Sitter spacetime. On the one hand, Noether's theorem assigns a set of conserved currents for each shift symmetric field, one current…

Computationally efficient classification system architecture is proposed. It utilizes fast tensor-vector multiplication algorithm to apply linear operators upon input signals . The approach is applicable to wide variety of recognition…

We study bosonic tensor field theories with sextic interactions in $d<3$ dimensions. We consider two models, with rank-3 and rank-5 tensors, and $U(N)^3$ and $O(N)^5$ symmetry, respectively. For both of them we consider two variations: one…

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

$N$ conformal theory models $WD^{(p)}_{3}$ coupled locally by their energy operators are analyzed by means of a perturbative renormalization group. New non-trivial fixed points are found.

We provide an explicit algorithm to calculate invariant tensors for the adjoint representation of the simple Lie algebra $sl(n)$, as well as arbitrary representation in terms of roots. We also obtain explicit formulae for the adjoint…

Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of…

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…

Using the proposed AdS/CFT correspondence, we calculate the correlators of operators of conformal field theory at the boundary of AdS$_{d+1}$ corresponding to the sine-Gordon model in the bulk.

Recently, many structured tensors are defined and their properties are discussed in the literature. In this paper, we introduce a new class of structured tensors, called exceptionally regular tensor, which is relevant to the tensor…

A study of an algorithm method capable to reveal anisotropic solutions of general scalar-tensor gravitation -including non-minimally couplings- is presented. It is found that it is possible to classify the behavior of the field of different…

Integral discriminants provide a simple and fundamental model for non-Gaussian integrals, associated with homogeneous polynomials of degree r in n variables. We argue that, in this context, the study of correlators is equally if not more…

We construct in detail an N=1, D=4 superspace with the superconformal algebra as the structure group and discuss its relation to prior component approaches and the existing Poincar\'e superspaces.

We propose a new constructive approach to the solutions of the conservation condition for the three-point conformal correlation function in the Osborn-Petkou formulation generalized by the authors for higher spins. We propose for…