English

Homological perspective on edge modes in linear Yang-Mills and Chern-Simons theory

High Energy Physics - Theory 2020-06-23 v2 Mathematical Physics Algebraic Topology math.MP

Abstract

We provide an elegant homological construction of the extended phase space for linear Yang-Mills theory on an oriented and time-oriented Lorentzian manifold MM with a time-like boundary M\partial M that was proposed by Donnelly and Freidel [JHEP 1609, 102 (2016)]. This explains and formalizes many of the rather ad hoc constructions for edge modes appearing in the theoretical physics literature. Our construction also applies to linear Chern-Simons theory, in which case we obtain the extended phase space introduced by Geiller [Nucl. Phys. B 924, 312 (2017)].

Keywords

Cite

@article{arxiv.1907.10651,
  title  = {Homological perspective on edge modes in linear Yang-Mills and Chern-Simons theory},
  author = {Philippe Mathieu and Laura Murray and Alexander Schenkel and Nicholas J. Teh},
  journal= {arXiv preprint arXiv:1907.10651},
  year   = {2020}
}

Comments

v2: 21 pages. New results on edge modes in linear Chern-Simons theory added. Final version to appear in Letters in Mathematical Physics