We study the conformally invariant quantum field theory in spaces of even dimension D ≥ 4. The conformal transformations of current j µ and energy-momentum tensor T µν are examined. It is shown that the set of conformal transformations of particular kind corresponds to the canonical (unlike anomalous) dimensions l j = D − 1 and l T = D of those fields. These transformations cannot be derived by...

This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics, [10]. The objects of study are scalar Riemannian quantities constructed out of the curvature and its covariant derivatives, whose integrals over compact manifolds are invariant under conformal changes of the underlying metric. Our main conclus...

We present a coordinate-invariant approach, based on a Pauli-Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in...

We construct explicit left invariant quaternionic contact structures on Lie groups with zero and non-zero torsion, and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of quaternionic contact manifolds not locally quaternionic contact conformal to the quaternionic sphere. We present a left invariant quaternionic contact structure on a seven dimensio...

We study global symmetries of generic 2D dilaton gravity models. Using a non-linear sigma model formulation we show that the unique theories admitting special conformal symmetries are the models with an exponential potential V ∝ e (S = 1 2π ∫ d2x √−g[Rφ+ 4λ2eβφ]), which include the model of Callan, Giddings, Harvey and Strominger (CGHS) as a particular though limiting (β = 0) case. These models...

We study the scaling behavior of the entanglement entropy of two-dimensional conformal quantum critical systems, i.e., systems with scale-invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that under quite general conditions, the entanglem...

We investigate what we call a conformal β-change in Finsler spaces, namely L(x, y) → * L(x, y) = e σ(x) L(x, y) + β(x, y) where σ is a function of x only and β(x, y) is a given 1-form. This change generalizes various types of changes: conformal changes, Randers changes and β-changes. Under this change, we obtain the relationships between some tensors associated with (M, L) and the corresponding...