Diffeomorphism Transformations Research Articles

Holographic trace anomaly and cocycle of Weyl group

The behavior of the divergent part of the bulk AdS/CFT effective action is considered with respect to the special finite diffeomorphism transformations acting on the boundary as a Weyl transformation of the boundary metric. The resulting 1-cocycle of the Weyl group is in full agreement with the 1-cocycle of the Weyl group obtained from the cohomological consideration of the effective action of the corresponding CFT.

Gauge group and reality conditions in Ashtekar’s complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekar's complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Dirac's method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Finite [formula omitted]3 transformations in a multi-time approach

Classical W 3 transformations are discussed as restricted diffeomorphism transformations ( W- Diff ) in two-dimensional space. We formulate them by using Riemannian geometry as a basic ingredient. The extended W 3 generators are given as particular combinations of Christoffel symbols. The defining equations of W- Diff are shown to depend on these generators explicitly. We also consider the issues of finite transformations, global SL(3) transformations and W- Schwarzians .

Diffeomorphism symmetry in phi4field theory

The diffeomorphism and Weyl transformations in the renormalized D-dimensional phi 4 theory are considered. The action functional including the sources of the operators phi 2 and phi 4 appears to be invariant with respect to these transformations with the appropriate choice of their form for the field and sources. For the generalized diffeomorphism transformation being some combination of diffeomorphism and Weyl transformations, the Ward identities for the renormalized Green functions of the field phi and operators phi 2, phi 4 are obtained. In the critical point they are similar to the Ward identities used in the 2D conformal field theory and enable one to prove the conformal invariance of phi 2 and phi 4 for arbitrary dimension D.

The measure for the supermoduli

We discuss the path integral measure for the heterotic and superstring, a basic ingredient for constructing amplitudes at every loop order. We find that a ghost supercurrent, which appears in the measure coupled to the gravitino zero modes due to the mixing of diffeomorphism and supersymmetry transformations, can be reabsorbed by a ghost field redefinition when also the gravitino Weyl transformation is carefully taken into account. Thus we obtain a result where only the matter supercurrent occurs.