The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d c = 2(N +1) is analyzed. We first exhibit the underlying group-theoretical clash between locality, gauge, Lorentz and conformal invariance requirements. " Improved "-traceless-stress tensors are then constructed; each violates one of the above criteria. How...

Using the asymptotic conformal invariance of perturbative QCD we derive the expression of the coupling of external states to all conformal spin p components of the forward elastic amplitude. Using the wave-function formalism for structure functions at small x, we derive the perturbative coupling of the virtual photon for p = 1 , which is maximal for linear transverse polarization. The non-pertu...

We show that in a two-dimensional σ-model whose fields only depend on one target space coordinate , the O(d, d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion). Duality invariance has proved to be an immensely fruitful concept in string theory. A particular aspect...

We give a new proof of the conformal invariance of the writhe of a knot from a conformal geometric vewpoint.

We show that in a two-dimensional σ-model whose fields only depend on one target space coordinate , the O(d, d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion). Duality invariance has proved to be an immensely fruitful concept in string theory. A particular aspect...