On the covariant formulation of gauge theories with boundaries
arXiv:2312.01918 · doi:10.1088/1361-6382/ad3ffc
Abstract
In the present article, we review the classical covariant formulation of Yang-Mills theory and general relativity in the presence of spacetime boundaries, focusing mainly on the derivation of the presymplectic forms and their properties. We further revisit the introduction of the edge modes and the conditions which justify them, in the context where only field-independent gauge transformations are considered. We particularly show that the presence of edge modes is not justified by gauge invariance of the presymplectic form, but rather by the condition that the presymplectic form is degenerate on the initial field space, which allows to relate this presymplectic form to the symplectic form on the gauge reduced field space via pullback.
arXiv comment47 pages; minor corrections; further references added
References in corpus (73)
- Black Hole Entropy is Noether Charge
- Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
- Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
- Invariant Variation Problems
- Soft Hair on Black Holes
- On BMS Invariance of Gravitational Scattering
- A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
- BMS supertranslations and Weinberg's soft graviton theorem
- A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
- New Symmetries of Massless QED
- Local subsystems in gauge theory and gravity
- Asymptotic symmetries and subleading soft graviton theorem
- Setting the boundary free in AdS/CFT
- Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
- Surface charge algebra in gauge theories and thermodynamic integrability
- The Statistical Mechanics of the (2+1)-Dimensional Black Hole
- Evidence for a New Soft Graviton Theorem
- Asymptotic Structure of Symmetry Reduced General Relativity
- Conserved charges of the extended Bondi-Metzner-Sachs algebra
- Superboost transitions, refraction memory and super-Lorentz charge algebra
- Extended Symmetries at the Black Hole Horizon
- Edge modes of gravity -- I: Corner potentials and charges
- Covariant phase space with boundaries
- Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
- Bondi-Sachs Formalism
- Local phase space and edge modes for diffeomorphism-invariant theories
- The Weyl BMS group and Einstein's equations
- Boundary dynamics and the statistical mechanics of the 2+1 dimensional black hole
- Extended corner symmetry, charge bracket and Einstein's equations
- Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
- Generalized BMS charge algebra
- Edge modes of gravity -- II: Corner metric and Lorentz charges
- BMS Supertranslations and Memory in Four and Higher Dimensions
- Null boundary phase space: slicings, news and memory
- Vacua of the gravitational field
- Embeddings and Integrable Charges for Extended Corner Symmetry
- Einstein-Yang-Mills theory : I. Asymptotic symmetries
- Isolated Surfaces and Symmetries of Gravity
- Edge modes of gravity. Part III. Corner simplicity constraints
- Color Memory
- Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases
- Conformal Edge Currents in Chern-Simons Theories
- Lorentz-diffeomorphism edge modes in 3d gravity
- Black Hole Entropy from BMS Symmetry at the Horizon
- A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter
- The Observer's Ghost: a field-space connection-form and its application to gauge theories and general relativity
- Centrally extended BMS4 Lie algebroid
- T-Witts from the horizon
- Horizon fluff, semi-classical black hole microstates - Log-corrections to BTZ entropy and black hole/particle correspondence
- Geometric formulation of the Covariant Phase Space methods with boundaries
- Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity
- Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates
- A Unified Geometric Framework for Boundary Charges and Particle Dressings
- Extensions of the asymptotic symmetry algebra of general relativity
- Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity
- Null Surface Thermodynamics
- Symmetries at Causal Boundaries in 2D and 3D Gravity
- Chiral Massive News: Null Boundary Symmetries in Topologically Massive Gravity
- Multipole expansion of gravitational waves: memory effects and Bondi aspects
- Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
- Matrix Quantization of Gravitational Edge Modes
- Covariant phase space for gravity with boundaries: metric vs tetrad formulations
- On Symplectic Form for Null Boundary Phase Space
- Boundary dynamics in gravitational theories
- Symplectic reduction of Yang-Mills theory with boundaries: from superselection sectors to edge modes, and back
- Edge modes without edge modes
- Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
- Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables
- Soft charges from the geometry of field space
- Bondi-Metzner-Sachs invariance and electric-magnetic duality
- On the definition of mass in general relativity: Noether charges and conserved quantities in diffeomorphism invariant theories
- Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences
- On the on-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries