Related papers: Reconstructing conformal field theoretical composi…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
We begin by reexamining the holographic reconstruction of scalar fields in four-dimensional anti-de Sitter spacetime, adopting a purely Lorentzian signature derivation, reproducing earlier results of HKLL and generalizing to arbitrary…
We show how bosonic (free field) representations for so-called degenerate conformal theories are built by singular vectors in Verma modules. Based on this construction, general expressions of conformal blocks are proposed. As an example we…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
A fully algebraic approach to reconstructing one-dimensional reflectionless potentials is described. A simple and easily applicable general formula is derived, using the methods of the theory of determinants. In particular, useful…
We construct the effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles $N$. It is given by a $\winf$ conformal field theory (with central charge $c=1$) that describes {\it exactly}…
Retrosynthesis plays a crucial role in the fields of organic synthesis and drug development, where the goal is to identify suitable reactants that can yield a target product molecule. Although existing methods have achieved notable success,…
We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)-dimensional conformal field theory (CFT) associated…
We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the…
We discuss the structure of 2D conformal field theories (CFT) at central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b…
The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal…
The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as…
We construct highest weight vectors of ${\widehat{\mathfrak{sl}_2}}_{,k+1} \oplus \mathsf{Vir}$ in tensor products of highest weight modules of ${\widehat{\mathfrak{sl}_2}}_{,k}$ and ${\widehat{\mathfrak{sl}_2}}_{,1}$, and thus for generic…
Wess-Zumino-Witten (WZW) models are among the most basic and most studied Conformal Field Theories (CFT). They have had a huge influence not only in physics but also in mathematics, in representation theory and geometry. However their…
In this paper we develop a general method for constructing 3-point functions in conformal field theory with affine Lie group symmetry, continuing our recent work on 2-point functions. The results are provided in terms of triangular…
The excitation spectrum of specific conformal field theories (CFT) with central charge $c=1$ can be described in terms of quasi-particles with charges $Q=-p,+1$ and fractional statistics properties. Using the language of Jack polynomials,…
We show that the noncommutative Wess-Zumino (NCWZ) Lagrangian with permutation terms in the interaction parts is renormalizable at one-loop level by only a wave function renormalization. When the non-commutativity vanishes, the logarithmic…
We present a comprehensive study of the effective Conformal Field Theory (CFT) describing the low energy excitations of a gas of spinless interacting fermions on a circle in the gapless regime (Luttinger liquid). Functional techniques and…
Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…
The method of large spin perturbation theory allows to analyse conformal field theories (CFT) by turning the crossing equations into an algebraic problem. We apply this method to a generic CFT with weakly broken higher spin (HS) symmetry,…