相关论文: A note on decoupling conditions for generic level …

We calculate fusion rules for the admissible representations of the affine superalgebra sl(2|1;C) at fractional level k=-1/2 in the Ramond sector. By representing 3-point correlation functions involving a singular vector as the action of…

We derive the fusion rules for a basic series of admissible representations of $\hat{sl}(3)$ at fractional level $3/p-3$. The formulae admit an interpretation in terms of the affine Weyl group introduced by Kac and Wakimoto. It replaces the…

Recently, exact agreement has been found between bulk and boundary three-point functions in AdS_3 x S^3 x T^4 with NSNS fluxes. This represents a non-trivial check of AdS/CFT correspondence beyond the supergravity approximation as it…

Working in the context of the proposed duality between 3D higher spin gravity and 2D W_N minimal model CFTs, we compute a class of four-point functions in the bulk and on the boundary, and demonstrate precise agreement between them. This is…

This is a set of notes which reviews and addresses issues in the SL(2,R) conformal field theory, while working primarily in a basis of vertex operators of definite weight under the affine algebra. Following a review of the H3 coset model…

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…

Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful…

We review the emergence of hypergeometric structures (of $F_4$ Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions $d > 2$. We illustrate the case of scalar 3- and 4-point functions.…

The logarithmic running of the gauge couplings alpha_1, alpha_2 and alpha_3, indicates that they may unify at some scale M_GUT ~ 10^16. This is often taken to imply that the standard model gauge group is embedded into some larger simple…

In cosmological perturbation theory it is convenient to use the scalar, vector, tensor (SVT) basis as defined according to how these components transform under 3-dimensional rotations. In attempting to solve the fluctuation equations that…

We present the details and first results of a new strategy for the determination of $\alpha_s(m_Z)$. By simultaneously decoupling 3 fictitious heavy quarks we establish a relation between the $\Lambda$-parameters of three-flavor QCD and…

Three-point functions of Wess-Zumino-Witten models are investigated. In particular, we study the level-dependence of three-point functions in the models based on algebras $su(3)$ and $su(4)$. We find a correspondence with…

Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…

Fusion rules for Wess-Zumino-Witten (WZW) models at fractional level can be defined in two ways, with distinct results. The Verlinde formula yields fusion coefficients that can be negative. These signs cancel in coset fusion rules, however.…

In a previous article, we define "connectivity weights" to be functions with these two properties: 1) They solve the three conformal Ward identities of conformal field theory (CFT) and a system of $2N$ null-state differential equations…

In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the…

We give a geometric description of the fusion rules of the affine Lie algebra su(2)_k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes…

The fusion products of admissible representations of the su(2) WZW model at the fractional level k=-4/3 are analysed. It is found that some fusion products define representations for which the spectrum of L_0 is not bounded from below.…

The quark and lepton mass patterns upset their naive unification. In this paper, a new approach to solve this problem is proposed. Model-independently, we find that a successful unification can be achieved. A mechanism is identified by…

We propose a new consistency condition for the compatibility of a gravitational effective field theory in AdS with a dual holographic description in terms of a family of large-$N$ CFTs. Using large-$N$ factorization of correlation functions…