We discuss Weyl (conformal) transformations in two-dimensional matterless dilaton gravity. We argue that both classical and quantum dilaton gravity theories are invariant under Weyl transformations. PACS number(s): 04.60.Kz, 04.20.Cv

The Grothendieck rings of finite dimensional representations of the basic classical Lie superalgebras are explicitly described in terms of the corresponding generalised root systems. We show that they can be interpreted as the subrings in the weight group rings invariant under the action of certain groupoids, which we call Weyl groupoids.

Some calculational errors in expressions derived previously by the first author for the effective action, or equivalently for the functional determinant, on sectors of a spherical cap are corrected. The formula for the change in the effective action under Weyl rescalings in the three dimensional case is also amended. October 1994

Let φ : M → Rn+p(c) be an n-dimensional submanifold in an (n + p)dimensional space form Rn+p(c) with the induced metric g. Willmore functional of φ is W (φ) = ∫M (S − nH2)n/2dv, where S = ∑ α,i, j (h α i j ) 2 is the square of the length of the second fundamental form, H is the mean curvature of M . The Weyl functional of (M, g) is ν(g) = ∫M |Wg|n/2dv, where |Wg|2 = ∑ i, j,k,l W 2 i jkl and Wi ...

Conformal invariant new forms of p-brane and Dp-brane actions are proposed. These are quadratic in ∂X for the p-brane case and for Dp-branes in the Abelian field strength. The fields content of these actions are: an induced metric, gauge fields, an auxiliary metric and an auxiliary scalar field. The proposed actions are Weyl invariant in any dimension and the elimination of the auxiliary metric...

Recently the first two authors [1] constructed an L∞-morphism using the S1-equivariant version of the Poisson Sigma Model (PSM). Its role in deformation quantization was not entirely clear. We give here a “good” interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors [5], [9].

In this work, we establish Weyl–Titchmarsh theory for symplectic difference systems. This paper extends classical Weyl–Titchmarsh theory and provides a foundation for studying spectral theory of symplectic difference systems. 2010 Elsevier Inc. All rights reserved.

Solutions to the four-dimensional Euclidean Weyl equation in the background of a general JNR N -instanton are known to be normalisable and regular throughout four-space. We show that these solutions are asymptotically given by a linear combination of simple singular solutions to the free Weyl equation, which can be interpreted as localised spinors. The ‘spinorial’ data parameterising the asympt...

In these notes, we present Kontsevich’s theorem on the deformation quantization of Poisson manifolds, his formality theorem and Tamarkin’s algebraic version of the formality theorem. We also introduce the necessary material from deformation theory.