Related papers: Finite Cutoff CFT's and Composite Operators

Effective field theories (EFTs) provide a powerful framework to parametrise unknown aspects of possible ultraviolet (UV) physics. For scalar fields in de Sitter space, however, new emergent phenomena can arise when the cut-off scale of the…

We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal…

We derive parametric integral representations for the general $n$-point function of scalar operators in momentum-space conformal field theory. Recently, this was shown to be expressible as a generalised Feynman integral with the topology of…

We consider various classes of bounded operators on the Fock space $F^2$ of Gaussian square integrable entire functions over the complex plane. These include Toeplitz (type) operators, weighted composition operators, singular integral…

We compute exactly various 4-point correlation functions of shortest scalar operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE to extract from these functions the exact expressions for the scaling dimensions and…

We consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity…

We demonstrate by explicit multi-loop calculation that \gamma-deformed planar N=4 SYM, supplemented with a set of double-trace counter-terms, has two nontrivial fixed points in the recently proposed double scaling limit, combining vanishing…

The large momentum expansion for the inverse propagator of the auxiliary field $\lambda(x)$ in the conformally invariant O(N) vector model is calculated to leading order in 1/N, in a strip-like geometry with one finite dimension of length…

We use the large N_f self consistency formalism to compute the $O(1/N_f)$ critical exponent corresponding to the renormalization of the flavour non-singlet twist two Wilson operators which arise in the operator product expansion of currents…

We present important characterizations of the Weighted Composition Operator over the Mittag Leffler space of entire functions. These characterizations include the Hilbert-Schmidt and Unitary char-acterizations of the Weighted Composition…

We consider application of the analytic functional approach to the conformal field theories associated with mean field theory and Wilson-Fisher fixed point. We study the constraints imposed by the crossing symmetry on the coefficients of…

Conformal multiplets of $\phi$ and $\phi^3$ recombine at the Wilson-Fisher fixed point, as a consequence of the equations of motion. Using this fact and other constraints from conformal symmetry, we reproduce the lowest nontrivial order…

For a topological space $X$ a topological contraction on $X$ is a closed mapping $f:X\to X$ such that for every open cover of $X$ there is a positive integer $n$ such that the image of the space $X$ via the $n$th iteration of $f$ is a…

We investigate the perturbative renormalisation of deformed conformal field theories from the Hamiltonian perspective. We discuss the relation with conformal perturbation theory, to which we provide an explicit match up to third order in…

We discuss three-dimensional $ \lambda\phi^4+\eta\phi^6 $ theory in the context of the 1/N expansion at finite temperature. We use the method of the composite operator (CJT) for summing a large sets of Feynman graphs. We analyse the…

Let $\varphi$ be a linear-fractional, non-automorphism self-map of $\mathbb{D}$ that fixes $\zeta \in \mathbb{T}$ and satisfies $\varphi^{\prime}(\zeta) \neq 1$ and consider the composition operator $C_{\varphi}$ acting on the Hardy space…

We show, within the framework of the Euclidean $\phi^4$-quantum field theory in four dimensions, that the Wilson operator product expansion (OPE) is not only an asymptotic expansion at short distances as previously believed, but even…

Given a critical quantum spin chain described by a conformal field theory (CFT) at long distances, it is crucial to understand the universal conformal data. One most important ingredient is the operator product expansion (OPE) coefficients,…

I demonstrate that the amplitude of the high-energy scattering can be factorized in a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators -- infinite gauge…

We study operator insertions into the $1/2$ BPS Wilson loop in ${\cal N}=4$ SYM theory and determine their two-point coefficients, anomalous dimensions and structure constants. The calculation is done for the first few lowest dimension…