We develop a formalism to evaluate generic scalar exchange diagrams in AdSd+1 relevant for the calculation of four-point functions in AdS/CFT correspondence. The result may be written as an infinite power series of functions of cross-ratios. Logarithmic singularities appear in all orders whenever the dimensions of involved operators satisfy certain relations. We show that the AdSd+1 amplitude c...

This paper is a continuation of [33] at which several coset subalgebras of the lattice VOA V2E8 were constructed and the relationship between such algebras with the famous McKay observation on the extended E8 diagram and the Monster simple group were discussed. In this article, we shall provide the technical details. We completely determine the structure of the coset subalgebras constructed and...

This work presents a first study of a radiative calculation for the gravitational axial anomaly in the massless Abelian Higgs model. The two loop contribution to the anomalous correlation function of one axial current and two energy-momentum tensors, 〈Aα(z)Tμν(y)Tρσ(x)〉, is computed at an order that involves only internal matter fields. Conformal properties of massless field theories are used i...

The conception of the conformal phase transiton (CPT), which is relevant for the description of non-perturbative dynamics in gauge theories, is introduced and elaborated. The main features of such a phase transition are established. In particular, it is shown that in the CPT there is an abrupt change of the spectrum of light excitations at the critical point, though the phase transition is cont...

Ĥ satisfies the Character Diagram shown in §1 and thus has natural transformations onto both closed differential forms with integral periods and integral cohomology. It was shown in [6] that an enriched version of the Weil homomorphism, carrying both an invariant polynomial and an associated integral homology class of the classifying space, naturally factors through Ĥ on its way to these target...

We discuss the relationship between the phase diagram of the Q = 0 state Potts model, the arboreal gas model, and the supersphere sigma model S = OSP (1/2)/OSP (0/2). We identify the Potts antiferromagnetic critical point with the critical point of the arboreal gas (at negative tree fugacity), and with a critical point of the sigma model. We show that the corresponding conformal theory on the s...

We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon e...

A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest-neighbor interactions, the vertices defining the model also interact along one of the diagonals of the lattice. This family of models includes in a special limit the standard six-vertex model. The exact solution of these models is an application of the matrix product ansatz introdu...

We study the relation between two sets of correlators in interacting quantum field theory on de Sitter space. The first are correlators computed using in-in perturbation theory in the expanding cosmological patch of de Sitter space (also known as the conformal patch, or the Poincaré patch), and for which the free propagators are taken to be those of the free Euclidean vacuum. The second are cor...

Abstract In general relativity (without matter), there is typically a one parameter family of static, maximally symmetric black hole solutions labeled by their mass. We show that are situations with many more holes. study asymptotically anti-de Sitter in six and seven dimensions having conformal boundary which product spheres cross time. the number families holes depends on ratio, λ , radii sph...