A low-energy limit of Yang-Mills theory on de Sitter space


Cork J., Kutluk E. S. , Lechtenfeld O., Popov A. D.

JOURNAL OF HIGH ENERGY PHYSICS, vol.2021, no.9, 2021 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 9
  • Publication Date: 2021
  • Doi Number: 10.1007/jhep09(2021)089
  • Title of Journal : JOURNAL OF HIGH ENERGY PHYSICS
  • Keywords: Effective Field Theories, Gauge Symmetry, Sigma Models, MANIFOLDS, GEOMETRY

Abstract

We consider Yang-Mills theory with a compact structure group G on four-dimensional de Sitter space dS(4). Using conformal invariance, we transform the theory from dS(4 )to the finite cylinder I x S-3, where I = (-pi/2, pi/2) and S-3 is the round three-sphere. By considering only bundles P -> I x S-3 which are framed over the temporal boundary partial derivative I x S-3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on partial derivative I x S-3. We study the consequences of the framing on the variation of the action, and on the Yang-Mills equations. This allows for an infinite-dimensional moduli space of Yang-Mills vacua on dS(4). We show that, in the low-energy limit, when momentum along I is much smaller than along S-3, the Yang-Mills dynamics in dS(4) is approximated by geodesic motion in the infinite-dimensional space M-vac of gauge-inequivalent Yang-Mills vacua on S-3. Since M-vac congruent to C-infinity (S-3, G)/G is a group manifold, the dynamics is expected to be integrable.