The decomposition of Global Conformal Invariants: On a conjecture of Deser and Schwimmer
نویسنده
چکیده
We present a proof of a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be scalar quantities whose integrals over compact manifolds remain invariant under conformal changes of the underlying metric. We prove that any such invariant can be expressed as a linear combination of a local conformal invariant, a divergence, and the Chern-Gauss-Bonnet integrand.
منابع مشابه
The Decomposition of Global Conformal Invariants : Some Technical
This paper forms part of a larger work where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the C...
متن کاملOn the decomposition of Global Conformal Invariants I
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...
متن کاملOn the decomposition of Global Conformal Invariants II
This paper is a continuation of [2], where we complete our partial proof of the Deser-Schwimmer conjecture on the structure of “global conformal invariants”. Our theorem deals with such invariants P (g) that locally depend only on the curvature tensor Rijkl (without covariant derivatives). In [2] we developed a powerful tool, the “super divergence formula” which applies to any Riemannian operat...
متن کاملSome new families of definite polynomials and the composition conjectures
The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...
متن کاملDecomposition of H*-Algebra Valued Negative Definite Functions on Topological *-Semigroups
In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...
متن کامل