We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface Σ that separates two subsystems of quantum strongly coupled N = 4 SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a clos...

We consider two level k WZNW models coupled to each other through a generalized Thirring-like current-current interaction. It is shown that in the large k limit, this interacting system can be presented as a two-parameter perturbation around a nonunitary WZNW model. The perturbation operators are the sigma model kinetic terms with metric related to the Thirring coupling constants. The renormali...

The aim of this paper to study the nature of spatial correlation of yields of agricultural crops. The focus is primarily on natural or non-anthropogenic spatial variation, patterns that cannot be explained by topography, by variety or treatment effects, or by agricultural practices. Conformal invariance implies stationarity and isotropy, and also determines the rate of decay of spatial correlat...

We show that there exist conformally invariant theories for all spins in d = 4 de Sitter space, namely the partially massless models with higher derivative gauge invariance under a scalar gauge parameter. This extends the catalog from the two known gauge models – Maxwell and partially massless spin 2 – to all spins.

Momentum space Ward identities are derived for the amputated n-point Green’s functions in 3 + 1 dimensional non-relativistic conformal field theory. For n = 4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Green’s functions) are considered. Any scale invariant 2-to-2 scattering amplitude is also conformally invariant. However, conformal invariance imposes constraints ...

Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, and in particular to construct the vertex operators for string emission as well as the supersymmetry charge. The calculation of string loop diagrams is sketched. We discuss how conformal methods can be ...

The word percolation, borrowed from the Latin, refers to the seeping or oozing of a liquid through a porous medium, usually to be strained. In this and related senses it has been in use since the seventeenth century. It was introduced more recently into mathematics by S. R. Broadbent and J. M. Hammersley ([BH]) and is a branch of probability theory that is especially close to statistical mechan...

A strategy for proving Riemann hypothesis is suggested. The vanishing of the Rieman Zeta reduces to an orthogonality condition for the eigenfunctions of a non-Hermitian operator D+ having the zeros of Riemann Zeta as its eigenvalues. The construction of D+ is inspired by the conviction that Riemann Zeta is associated with a physical system allowing conformal transformations as its symmetries. T...