Related papers: Conformal Three-Point Correlation Functions from t…
We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we generalize the determinant representation, found by Foda for the three-point functions of the…
We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for…
We develop an approach to construct local bulk operators in a CFT to order $1/N^2$. Since 4-point functions are not fixed by conformal invariance we use the OPE to categorize possible forms for a bulk operator. Using previous results on…
We derive an asymptotic formula for operator product expansion coefficients of heavy operators in two dimensional conformal field theory. This follows from modular invariance of the genus two partition function, and generalises the…
We study exact correlation functions of N=4 SYM at zero coupling. It has been known that it is convenient to label local gauge invariant operators by irreducible representations of symmetric groups/Brauer algebras. We first review the…
We discuss a correlation function factorization, which relates a three-point function to the square root of three two-point functions. This factorization is known to hold for certain scaling operators at the two-dimensional percolation…
We extend the OPE-based renormalization algorithm to composite operators with operator mixing, focusing on scalar operators in $\phi^4$ and $\phi^3$ models. Using the OPE of operators with a fundamental field, we show that the $Z$-factors…
We compute three-point correlation functions in the near-extremal, near-horizon region of a Kerr black hole, and compare to the corresponding finite-temperature conformal field theory correlators. For simplicity, we focus on scalar fields…
We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model…
We explore the use of optimized operators, designed to interpolate only a single meson eigenstate, in three-point correlation functions with a vector-current insertion. These operators are constructed as linear combinations in a large basis…
$T\bar{T}$-deformed CFTs are known to possess nonlocal conformal symmetries that do not act tractably on the undeformed local operators. In this paper, we explicitly construct two distinct classes of operators: (i) dressed operators, which…
The requirements of conformal invariance for two and three point functions for general dimension $d$ on flat space are investigated. A compact group theoretic construction of the three point function for arbitrary spin fields is presented…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
We compute three-point functions between one large classical operator and two large BPS operators at weak coupling. We consider operators made out of the scalars of N=4 SYM, dual to strings moving in the sphere. The three-point function…
The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
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 calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory to one-loop order. In order to carry out the calculations we project the indices of the spin j operator to…
We discuss conformal manifolds for conformal field theories with boundaries or defects. Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions…
A common problem in econometrics, statistics, and machine learning is to estimate and make inference on functions that satisfy shape restrictions. For example, distribution functions are nondecreasing and range between zero and one, height…