English

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).

Keywords

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

R2 v1 2026-06-21T15:27:45.576Z