An Extension of Pohlmeyer's Theorem
High Energy Physics - Theory
2011-03-28 v3 Strongly Correlated Electrons
High Energy Physics - Phenomenology
Abstract
Applying the Exact Renormalization Group to scalar field theory in Euclidean space of general (not necessarily integer) dimension, it is proven that the only fixed-point with vanishing anomalous dimension is the Gaussian one. The proof requires positivity of the two-point connected correlation function together with a technical assumption concerning solutions of the flow equation. The method, in which the representation of the flow equation as a heat equation plays a central role, extends directly to non-gauge theories with arbitrary matter content (though non-linear sigma models are beyond the scope of the current method).
Cite
@article{arxiv.1005.4680,
title = {An Extension of Pohlmeyer's Theorem},
author = {Oliver J. Rosten},
journal= {arXiv preprint arXiv:1005.4680},
year = {2011}
}
Comments
v1: 29 pages; v2: 30 pages, minor tweaks; v3: published with very minor changes