Related papers: Three-Point Functions in N=4 SYM Theory at One-Loo…

We consider four-point correlation functions of protected single-trace scalar operators in planar N = 4 supersymmetric Yang-Mills (SYM). We conjecture that all loop corrections derive from an integrand which enjoys a ten-dimensional…

The two point integrals contributing to the self energy of a particle in a three dimensional quantum field theory are calculated to two loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to…

We (re)derive the propagators and Feynman rules for the massless scalar and vector multiplets in N=2 Projective Superspace ('Projective Hyperspace'). With these, we are able to calculate both the divergent and finite parts of 2, 3 & 4-point…

We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2…

We compute analytically the three-loop correlation function of the local operator $\text{tr} \, \phi^3$ inserted into three on-shell states, in maximally supersymmetric Yang-Mills theory. The result is expressed in terms of Chen iterated…

Using the {\em cutting and sewing} procedure we show how to get Feynman diagrams, up to two-loop order, of $\Phi^{4}$-theory with an internal SU(N) symmetry group, starting from tachyon amplitudes of the open bosonic string theory. In a…

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…

A new derivation is given of four-point functions of charge $Q$ chiral primary multiplets in N=4 supersymmetric Yang-Mills theory. A compact formula, valid for arbitrary $Q$, is given which is manifestly superconformal and analytic in the…

We consider ${\mathcal N}=1$ superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet $S_{\alpha}$ and study three-point functions involving such an operator. A conserved spinor current…

We derive the three-loop dilatation operator of the flavor SU(2) subsector of N=4 supersymmetric Yang-Mills theory in the planar limit by a direct Feynman diagram calculation in N=1 superspace. The transcendentality three contributions…

In a previous paper, arXiv:1204.3096, we have shown that the fully dynamical three-point correlation functions of BMN operators are identical at the tree level in the planar limit of perturbative field theory and, on the string theory side,…

We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building…

We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and…

Besides solving the spectral problem of $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory, integrability also provides us with tools to compute the structure constants of the theory, most prominently through the hexagon formalism. We show that,…

We study three-dimensional conformal field theories with a large-$N$ limit. Leveraging the framework of slightly broken higher-spin symmetry, we bootstrap correlation functions between the single-trace, local operators and straight,…

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

We study correlation functions on the Coulomb branch of planar $\mathcal{N} = 4$ super-Yang- Mills theory (SYM), and their relationship with integrability, the operator product expansion (OPE), the sum rule, the large charge expansion, and…

Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…

We develop a general formalism to study the three-point correlation functions of conserved higher-spin supercurrent multiplets $J_{\alpha(r) \dot{\alpha}(r)}$ in 4D ${\cal N}=1$ superconformal theory. All the constraints imposed by ${\cal…

We classify the 3-point functions of local gauge-invariant single-trace operators in the scalar sector of planar N=4 supersymmetric Yang-Mills involving at least one su(3) operator. In the case of two su(3) and one su(2) operators, the…