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

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 $M$ with a time-like boundary $\partial M$ 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)].

arXiv commentv2: 21 pages. New results on edge modes in linear Chern-Simons theory added. Final version to appear in Letters in Mathematical Physics

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Cited by in corpus (11)

• Edge modes as reference frames and boundary actions from post-selection
• Extended actions, dynamics of edge modes, and entanglement entropy
• Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches
• Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method
• Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions
• Dressing vs. Fixing: On How to Extract and Interpret Gauge-Invariant Content
• On the Meaning of Local Symmetries: Epistemic-Ontological Dialectics
• The dressing field method for diffeomorphisms: a relational framework
• A low-energy limit of Yang-Mills theory on de Sitter space
• Yang-Mills-Stueckelberg Theories, Framing and Local Breaking of Symmetries
• Boundary electromagnetic duality from homological edge modes