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A q-analogue of four dimensional conformally invariant field theory based on the quantum algebra U_{q}(so(4,2)) is proposed. The two- and three-point correlation functions are calculated. The construction is elaborated in order to fit the…
We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational,…
We consider two instances of boundary conditions for massless scalars on $AdS_2$ that interpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessing invariance under the full $SL(2;\mathds{R})$ conformal…
The class of effective actions exactly reproducing the conformal anomaly in 4D is considered. It is demonstrated that the freedom within this class can be fixed by the choice of the conformal gauge. The conformal invariant part of the…
We implement the O(d,d,Z) transformations of T-duality as automorphisms of the operator algebras of Conformal Field Theories. This extends these transformations to arbitrary field configurations in the deformation class.
We calculate the leading contributions to the connected two-point functions of protected scalar operators in the defect version of N=4 SYM theory which is dual to the D5-D3 probe-brane system with k units of background gauge field flux.…
In this paper we study the four-point correlation function of the energy-momentum supermultiplet in theories with N=4 superconformal symmetry in four dimensions. We present a compact form of all component correlators as an invariant of a…
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis.…
Structure constants of Operator Algebras for the SL(2) degenerate conformal field theories are calculated.
We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…
We construct in detail an N=1, D=4 superspace with the superconformal algebra as the structure group and discuss its relation to prior component approaches and the existing Poincar\'e superspaces.
The bosonic actions for M2, D3 and M5 branes in their own d-dimensional near-horizon background are given in a manifestly SO(p+1,2) x SO(d-p-1) invariant form (p=2,3,5). These symmetries result from a breakdown of ISO(d,2) (with d=10 for D3…
Extending previous work on 2 -- and 3 -- point functions, we study the 4 -- point function and its conformal block structure in conformal quantum mechanics CFT$_1$, which realizes the SO(2,1) symmetry group. Conformal covariance is…
Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u,v. A recurrence relation for the function corresponding to the…
We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal…
We systematically derive the consistency relations associated to the non-linearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearly-realized de Sitter subalgebra. These identities relate…
In this article, we continue the investigation of hep-th 1611.02179 regarding iterative properties of dual conformal integrals in higher dimensions. In d=4, iterative properties of four and five point dual conformal integrals manifest…
We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system…