We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR’s of the conformal groups with Lie algebras so(2, d). We classify gauge theories invariant under so(2, d), both integral and half-integral spins. A similar analysis is carried out for the algebras so(2n). We study new unitary modules of the conformal algebra in d > 4, that have no analogue for d ≤ 4 as they c...

1 Kasner, "Conformal Classification of Analytic Arcs or Elements, Poincare's Local Problem of Conformal Geometry," Trans. Am. Math. Soc., 16, 333-349 (1915). The theory of a pair of regular arcs, including the horn angle, is given in "Conformal Geometry," Proceedings Cambridge International Congress Mathematicians, 1912, and a paper appearing in Scripta Mathematica, 1945. 2 Kasner and De Cicco,...

This paper defines two new extrinsic curvature quantities on the corner of a four-dimensional Riemannian manifold with corner. One these is pointwise conformal invariant, and transformation other governed by linear second-order conformally invariant partial differential operator. The Gauss-Bonnet theorem then stated in terms quantities.

In this paper, we study Hölder-continuous linear cocycles over transitive Anosov diffeomorphisms. Under various conditions of relative pinching we establish properties including existence and continuity of measurable invariant subbundles and conformal structures. We use these results to obtain criteria for cocycles to be isometric or conformal in terms of their periodic data. We show that if th...

We describe the generators of κ-conformal transformations, leaving invariant the κ-deformed d’Alembert equation. In such a way one obtains the conformal extension of the off-shell spin zero realization of κ-deformed Poincaré algebra. Finally the algebraic structure of κ-deformed conformal algebra is discussed. The paper is dedicated to the memory of Professor Jan Rzewuski and will appear in the...

It is well known that a local, unitary Poincaré-invariant 2D quantum field theory with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this Letter, we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left con...

Recent work in even-dimensional conformal geometry [1],[3], [4], [6] has revealed the importance of conformally invariant powers of the Laplacian on a conformal manifold; that is, of operators Pk whose principal part is the same as ∆ k with respect to a representative of the conformal structure. These invariant powers of the Laplacian were first defined in [5] in terms of the Fefferman-Graham [...

Using the conformal compensator superfields of N=2 D=4 supergravity, the Type IIB S-duality transformations are expressed as a linear rotation which mixes the compensator and matter superfields. The classical superspace action for D=4 compactifications of Type IIB supergravity is manifestly invariant under this transformation. Furthermore, the introduction of conformal compensators allows a Fra...

We have used the results of renormalization of a two-dimensional quantum stress tensor to develop a conformally invariant dynamical model. The model requires the consideration of those conformal frames in which there exists a correspondence between the trace anomaly and a cosmological constant. We apply this model to a two dimensionalSchwarzschild (-de Sitter) spacetime to show that in these co...

At high energy scale the only quantum effect of any asymptotic free and asymptoti-cally conformal invariant GUT is the trace anomaly of the energy-momentum tensor. Anomaly generates the new degree of freedom, that is propagating conformal factor. At lower energies conformal factor starts to interact with scalar field because of the violation of conformal invari-ance. We estimate the effect of s...