Related papers: Polylogarithm Identities in a Conformal Field Theo…

In 1925 Elie Cartan described `triality' \cite{CARTAN25}, \cite{CARTAN} as a symmetry between SO$(8; \mathbb{C})$ vectors and the two types of Spin$(8; \mathbb{C})$ spinor. It is known that the reduced generators of the Clifford algebra…

For a conformal theory it is natural to seek the conformal moduli space, M_c to which it belongs, generated by the exactly marginal deformations. By now we should have the tools to determine M_c in the presence of enough supersymmetry. Here…

We calculate a set of conformal correlators in the critical $O(N)$ vector model in $2<d<6$ dimensions. We focus on the correlators involving the Hubbard-Stratonovich field $s$, and its composite form $s^2$. In the process, we report a…

We observe that conformal blocks of scalar 4-point functions in a $d$-dimensional conformal field theory can mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled…

We analyse the fusion of representations of the triplet algebra, the maximally extended symmetry algebra of the Virasoro algebra at c=-2. It is shown that there exists a finite number of representations which are closed under fusion. These…

We study the structure of the four-point correlation function of the lowest-dimension 1/2 BPS operators (stress-tensor multiplets) in the (2,0) six-dimensional theory. We first discuss the superconformal Ward identities and the…

In complex vector spaces maximal sets of equiangular lines, known as SICs, are related to real quadratic number fields in a dimension dependent way. If the dimension is of the form $n^2+3$ the base field has a fundamental unit of negative…

We study four-dimensional superconformal field theories coupled to three-dimensional superconformal boundary or defect degrees of freedom. Starting with bulk N=2, d=4 theories, we construct abelian models preserving N=2, d=3 supersymmetry…

We formulate new boundary conditions that prove well defined variational principle and finite response functions for conformal gravity (CG). In the Anti--de Sitter/conformal field theory framework, gravity theory that is considered in the…

We show that the exactly solved low-temperature branch of the two-dimensional O($n$) model is equivalent with an O($n$) model with vacancies and a different value of $n$. We present analytic results for several universal parameters of the…

The Euklidean correlation functions and vacuum expectation values of products of field operators of some Lorentz spin and dimension are expressed through Mellin amplitudes which depend on complex dimensions subject to linear constraints.…

We prove new identities betweenthe values of Rogers dilogarithm function and describe a connection between these identities and spectra in conformal field theory.

All the supersymmetric configurations of pure, ungauged, N=4,d=4 supergravity are classified in a formalism that keeps manifest the S and T dualities of the theory. We also find simple equations that need to be satisfied by the…

A general discussion of the conformal Ward identities is presented in the context of logarithmic conformal field theory with conformal Jordan cells of rank two. The logarithmic fields are taken to be quasi-primary. No simplifying…

We investigate $O(N)$-symmetric vector field theories in the double scaling limit. Our model describes branched polymeric systems in $D$ dimensions, whose multicritical series interpolates between the Cayley tree and the ordinary random…

The simplicity and the efficiency of a quasi-analytical method for solving nonlinear ordinary differential equations (ODE), is illustrated on the study of anharmonic oscillators (AO) with a potential $V(x) =\beta x^{2}+x^{2m}$ ($m>0$). The…

We determine the symmetries of four different theories: I) Galilean Electrodynamics (GED), II) GED coupled to 5 free static scalar fields, III) Galilean Yang-Mills (GYM), and IV) GYM coupled to 5 interacting scalar fields. We correct some…

We renormalize various scalar field theories with a $\phi^n$ self interaction such as $n$ $=$ $5$, $7$ and $9$ in their respective critical dimensions which are non-integer. The renormalization group functions for the $O(N)$ symmetric…

Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the…

In this first of four articles, we study a homogeneous system of $2N+3$ linear partial differential equations (PDEs) in $2N$ variables that arises in conformal field theory (CFT) and multiple Schramm-Lowner evolution (SLE). In CFT, these…