Conformal invariance of white noise

Invariance of the White Noise for Kdv

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space bbp,∞, sp < −1, contains the support of the white noise. Then, we prove local well-posedness in bbp,∞ for p = 2+, s = − 1 2 + such that sp < −1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the i...

Higher Powers of White Noise and Conformal Field Theory

Abstract. The Virasoro–Zamolodchikov Lie algebra w∞ has been widely studied in string theory and in conformal field theory. The renormalized higher (≥ 3) powers of quantum white noise (RHPWN) algebra has been recently investigated in quantum probability. We prove that, after introducing a new renormalization technique, the RHPWN Lie algebra can be identified with a second quantization of the w∞...

Conformal invariance from non-conformal gravity

We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of non-conformal (Einstein) gravity. As an ‘existence proof’ that this is indeed possible we show how to derive N = 4 super Yang Mills theory with any compact gauge group G from non-conformal gauged N = 4 supergravity as a special flat space limit. We stress the role that the anticipa...

Chapter 18 Conformal Invariance

At the beginning of the semester we motivated our investigation of symmetries by illustrating that, given differential equations which were symmetric, the solutions had to transform into each other under the symmetries as a representation of the symmetry. The first illustrations considered Schrödinger equations with symmetric potentials, such as the electrons in the spherically symmetric potent...

Conformal invariance of domino tiling