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

Mathieu, Philippe; Murray, Laura; Schenkel, Alexander; Teh, Nicholas J.


Philippe Mathieu

Laura Murray

Nicholas J. Teh


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 @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.


Mathieu, P., Murray, L., Schenkel, A., & Teh, N. J. (2020). Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory. Letters in Mathematical Physics, 110, 1559–1584.

Journal Article Type Article
Acceptance Date Feb 7, 2020
Online Publication Date Feb 21, 2020
Publication Date 2020-07
Deposit Date Feb 17, 2020
Publicly Available Date Feb 22, 2021
Journal Letters in Mathematical Physics
Print ISSN 0377-9017
Electronic ISSN 1573-0530
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 110
Pages 1559–1584
Keywords Mathematical Physics; Statistical and Nonlinear Physics
Public URL
Publisher URL
Additional Information Received: 2 August 2019; Revised: 10 January 2020; Accepted: 7 February 2020; First Online: 21 February 2020; : ; : On behalf of all authors, the corresponding author states that there is no conflict of interest.


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