155 research outputs found
Boundary charges in gauge theories: using Stokes theorem in the bulk
Boundary charges in gauge theories (like the ADM mass in general relativity)
can be understood as integrals of linear conserved n-2 forms of the free theory
obtained by linearization around the background. These forms are associated
one-to-one to reducibility parameters of this background (like the time-like
Killing vector of Minkowski space-time). In this paper, closed n-2 forms in the
full interacting theory are constructed in terms of a one parameter family of
solutions to the full equations of motion that admits a reducibility parameter.
These forms thus allow one to apply Stokes theorem without bulk contributions
and, provided appropriate fall-off conditions are satisfied, they reduce
asymptotically near the boundary to the conserved n-2 forms of the linearized
theory. As an application, the first law of black hole mechanics in
asymptotically anti-de Sitter space-times is derived.Comment: 17 pages Latex file, improved presentation, main results unchanged,
additional section on first law, additional reference
A note on the BRST cohomology of the extended antifield formalism
The relevance of the BRST cohomology of the extended antifield formalism is
briefly discussed along with standard homological tools needed for its
computation.Comment: 10 pages Latex file, Proceedings of the spring school "Q.F.T.,
Supersymmetry and Superstrings" in Calimanesti, Romania, April 199
Refining the anomaly consistency condition
In the extended antifield formalism, a quantum BRST differential for
anomalous gauge theories is constructed. Local BRST cohomological classes are
characterized, besides the form degree and the ghost number, by the length of
their descents and of their lifts, and this both in the standard and the
extended antifield formalism. It is shown that during the BRST invariant
renormalization of a local BRST cohomological class, the anomaly that can
appear is constrained to be a local BRST cohomological class with a shorter
descent and a longer lift than the given class. As an application of both
results, a simple approach to the Adler-Bardeen theorem for the non abelian
gauge anomaly is proposed. It applies independently of the gauge fixing, of
power counting restrictions and does not rely on the use of the Callan-Symanzik
equation.Comment: 20 pages RevTex fil
Black hole entropy from non-proper gauge degrees of freedom: II. The charged vacuum capacitor
The question which degrees of freedom are responsible for the classical part
of the Gibbons-Hawking entropy is addressed. A physical toy model sharing the
same properties from the viewpoint of the linearized theory is a charged vacuum
capacitor. In Maxwell's theory, the gauge sector including ghosts is a
topological field theory. When computing the grand canonical partition function
with a chemical potential for electric charge in the indefinite metric Hilbert
space of the BRST quantized theory, the classical contribution originates from
the part of the gauge sector that is no longer trivial due to the boundary
conditions required by the physical set-up. More concretely, in the benchmark
problem of a planar charged vacuum capacitor, we identify the degrees of
freedom that, in the quantum theory, give rise to an additional contribution to
the standard black body result proportional to the area of the plates, and that
allow for a microscopic derivation of the thermodynamics of the charged
capacitor.Comment: 27 pages, V2: improved discussion of thermodynamics in section 2,
references added, no other change
Higher order cohomological restrictions on anomalies and counterterms
Using a regularization with the properties of dimensional regularization,
higher order local consistency conditions on one loop anomalies and divergent
counterterms are given. They are derived without any a priori assumption on the
form of the BRST cohomology and can be summarized by the statements that (i)
the antibracket involving the first order divergent counterterms, respectively
the first order anomaly, with any BRST cocycle is BRST exact, (ii) the first
order divergent counterterms can be completed into a local deformation of the
solution of the master equation and (iii) the first order anomaly can be
deformed into a local cocycle of the deformed solution.Comment: 11 pages Latex file, mistake in assumption 2 forces a version limited
to one loop considerations with a different derivation of main result
A general non renormalization theorem in the extended antifield formalism
In the context of algebraic renormalization, the extended antifield formalism
is used to derive the general forms of the anomaly consistency condition and of
the Callan-Symanzik equation for generic gauge theories. A local version of the
latter is used to derive sufficient conditions for the vanishing of beta
functions associated to terms whose integrands are invariant only up to a
divergence for an arbitrary non trivial non anomalous symmetry of the
Lagrangian. These conditions are independent of power counting restrictions and
of the form of the gauge fixation.Comment: 25 pages Latex file, major revision and extensio
Centrally extended BMS4 Lie algebroid
We explicitly show how the field dependent 2-cocycle that arises in the
current algebra of 4 dimensional asymptotically flat spacetimes can be used as
a central extension to turn the BMS4 Lie algebra, or more precisely, the BMS4
action Lie algebroid, into a genuine Lie algebroid with field dependent
structure functions. Both a BRST formulation, where the extension appears as a
ghost number 2 cocyle, and a formulation in terms of vertex operator algebras
are introduced. The mapping of the celestial sphere to the cylinder then
implies zero mode shifts of the asymptotic part of the shear and of the news
tensor.Comment: 17 pages Latex file, typos corrected in version
The Coulomb solution as a coherent state of unphysical photons
In the context of the problem of what micro-states are responsible for the
entropy of black holes, we consider as a physical toy model the electromagnetic
Coulomb solution. By quantizing the electromagnetic field in the presence of an
external source of charge Q, the quantum state corresponding to the Coulomb
solution is identified as a coherent state of longitudinal and temporal photons
in a Hilbert space with negative norm states.Comment: 5 pages Latex file, Proceedings of the 2nd School on Quantum Gravity
and Quantum Geometry, Corfu 2009. Cosmetic changes, agrees with version to be
published
Notes on the BMS group in three dimensions: II. Coadjoint representation
The coadjoint representation of the BMS group, which governs the
covariant phase space of three-dimensional asymptotically flat gravity, is
investigated. In particular, we classify coadjoint BMS orbits and show that
intrinsic angular momentum is free of supertranslation ambiguities. Finally,
the link with induced representations upon geometric quantization is discussed.Comment: 22 pages, references added, accepted for publication in JHEP. v3:
Minor typos corrected, matches published versio
Isomorphisms between the Batalin-Vilkovisky antibracket and the Poisson bracket
One may introduce at least three different Lie algebras in any Lagrangian
field theory : (i) the Lie algebra of local BRST cohomology classes equipped
with the odd Batalin-Vilkovisky antibracket, which has attracted considerable
interest recently~; (ii) the Lie algebra of local conserved currents equipped
with the Dickey bracket~; and (iii) the Lie algebra of conserved, integrated
charges equipped with the Poisson bracket. We show in this paper that the
subalgebra of (i) in ghost number and the other two algebras are
isomorphic for a field theory without gauge invariance. We also prove that, in
the presence of a gauge freedom, (ii) is still isomorphic to the subalgebra of
(i) in ghost number , while (iii) is isomorphic to the quotient of (ii) by
the ideal of currents without charge. In ghost number different from , a
more detailed analysis of the local BRST cohomology classes in the Hamiltonian
formalism allows one to prove an isomorphism theorem between the antibracket
and the extended Poisson bracket of Batalin, Fradkin and Vilkovisky.Comment: 36 pages Latex fil
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