Surface charge algebra in gauge theories and thermodynamic integrability

By G. Barnich, G. Compère. 2007

318 citations recorded by the source corpus.

Surface charges and their algebra in interacting Lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a Pfaff system. Integrability is governed by Frobenius’ theorem and the charges associated with the derived symmetry algebra are shown to vanish. In the asymptotic context, we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended. Comparison with Hamiltonian and covariant phase space methods is made. All approaches are shown to agree for exact solutions and symmetries while there are differences in the asymptotic context.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cda7067b17a0b384e721bb1eb09d892675e2c9ea

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Andrew Strominger
2. G. Barnich
3. Adrien Fiorucci
4. Cédric Troessaert
5. Wei Song
6. G. Compère
7. Thomas Hartman
8. A. Maloney

In Nuclear and High Energy Physics

1. Andrew Strominger
2. Thomas Hartman
3. G. Compère
4. Wei Song
5. L. Donnay
6. Adrien Fiorucci
7. A. Maloney
8. G. Barnich

In Statistical and Nonlinear Physics

1. Andrew Strominger
2. Thomas Hartman
3. G. Compère
4. Wei Song
5. Adrien Fiorucci
6. G. Barnich
7. L. Donnay
8. Cédric Troessaert

Citations in the corpus

• No dynamics in the extremal Kerr throat (2009, methodology): “Following [3], we will adopt the covariant phase space formalism of [26, 45], in which the symplectic current for metric”
• Central charges in extreme black hole/CFT correspondence (2009, background): “24) where the second line has been obtained from [19, 20].”
• Edge modes of gravity. Part I. Corner potentials and charges (2020, background): “Throughout the years, a very substantial amount of work has been dedicated to the study of these corner charges, their algebra, and their possible physical applications [19–30].”
• Hidden Conformal Symmetry of the Kerr Black Hole (2010, background): “In some cases, such central charges can be derived from an analysis of the asymptotic symmetry group [20,12,21,22].”
• CFT Duals for Extreme Black Holes (2008, methodology): “To compute the charges associated with asymptotic symmetries, we use the formalism of [12,13].”
• Advanced Lectures on General Relativity (2018, methodology): “The cohomological formalism for defining the surface charges (and in particular the proof of uniqueness or “Generalized Noether theorem") was developed in [3, 17, 7].”
• Extended symmetries at the black hole horizon (2016, methodology): “In our case, it is not necessary to introduce any constant to be ulteriorly set to the Planck scale, but our expressions for the charges smoothly follows from the covariant approach [29, 30].”
• Aspects of the BMS/CFT correspondence (2010, methodology): “In addition, the covariant expression for the surface charg es used above coincides onshell with those of the Hamiltonian formalism [56, 57].”
• New boundary conditions for AdS3 (2013, methodology): “The asymptotic charges and asymptotic symmetry algebra can be obtained using the formalism of [36, 37, 40, 41].”
• Chiral gravity, log gravity, and extremal CFT (2009, methodology): “Our expression follows from the covariant formalism [37, 38], which is based on [39] and has been developed in great detail for a wide variety of applications in [40].”
• Warped Conformal Field Theory (2012, background): “In the covariant formalism [80, 81, 82], the infinitesimal charge associated to an asymptotic Killing vector ζ is”
• Near Extremal Kerr Entropy from AdS(2) Quantum Gravity (2009, unknown): “1 acastro@physics.mcgill.ca 2 larsenf@umich.edu”
• BMS charge algebra (2011, background): “In the covariant approach, one can show a similar result [10, 12] .”
• Kerr/CFT Correspondence (2008, background): “deviations h of the metric are not subleading, the charges can have nonlinear corrections, which must be carefully considered. For this purpose the covariant formalism of Barnich, Brandt and Comp`ere [34, 35], based on [36, 37, 38, 39, 40, 41] and further developed in [42, 43], is the most complete ”