Searcharxiv⌕ Search

arXiv subjects

M. Henneaux

Publications and source records attributed to M. Henneaux.

At least 37 records · Page 2Linked to original sources
arXiv1997

A note on the gauge symmetries of pure Chern-Simons theories with p-form gauge fields

The gauge symmetries of pure Chern-Simons theories with p-form gauge fields are analyzed. It is shown that the number of independent gauge symmetries depends crucially on the parity of p. The case where p is odd appears to be a direct generalization of the p=1 case and presents the remarkable feature that the timelike diffeomorphisms can be expressed in terms of the spatial diffeomorphisms and the internal gauge symmetries. By constrast, the timelike diffeomorphisms may be an independent gauge symmetry when p is even. This happens when the number of fields and the spacetime dimension fulfills an algebraic condition which is explicitely written.

gr-qc↗
arXiv1997

Duality, Self-Duality, Sources and Charge Quantization in Abelian N-Form Theories

We investigate duality properties of N-form fields, provide a symmetric way of coupling them to electric/magnetic sources, and check that these charges obey the appropriate quantization requirements. First, we contrast the D=4k case, in which duality is a well-defined SO(2) rotation generated by a Chern-Simons form leaving the action invariant, and D=4k+2 where the corresponding ostensibly SO(1,1) rotation is not only not an invariance but does not even have a generator. When charged sources are included we show explicitly in the Maxwell case how the usual Dirac quantization arises in a fully symmetric approach attaching strings to both types of charges. Finally, for D=4k+2 systems, we show how charges can be introduced for self-dual (2k)-forms, and obtain the D=4k models with sources by dimensional reduction, tracing their duality invariance to a partial invariance in the higher dimensions.

hep-th↗
arXiv1996

Electric-Magnetic Black Hole Duality

We generalize duality invariance for the free Maxwell action in an arbitrary background geometry to include the presence of electric and magnetic charges. In particular, it follows that the actions of equally charged electric and magnetic black holes are equal.

hep-th↗
arXiv1995

The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant

Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant. This is because (i) Chern-Simons theory with a gauge group $SL(2,R) \times SL(2,R)$ on a space-time with a cylindrical boundary is equivalent to the non-chiral $SL(2,R)$ WZW model; and (ii) the anti-de Sitter boundary conditions implement the constraints that reduce the WZW model to the Liouville theory.

gr-qc↗
arXiv1995

Gauge Properties of Conserved Currents in Abelian Versus Nonabelian Theories

We clarify the physical origin of the difference between gauge properties of conserved currents in abelian and nonabelian theories. In the latter, but not in the former, such currents can always be written on shell as gauge invariants modulo identically conserved, superpotential, terms. For the ``isotopic" vector and the stress tensor currents of spins 1 and 2 respectively, we explain this difference by the fact that the non-abelian theories are just the self-coupled versions of the abelian ones using these currents as sources. More precisely, we indicate how the self-coupling turns the non-invariantizable abelian conserved currents into (on-shell) superpotentials. The fate of other conserved currents is also discussed.

hep-th↗
arXiv1994

General solution of the Wess-Zumino consistency condition for Einstein gravity

The Wess-Zumino consistency condition for four-dimensional Einstein gravity is investigated in the space of local forms involving the fields, the ghosts, the antifields and their derivatives. Its general solution is constructed for all values of the form degree and of the ghost number. It is shown in particular that the antifields (= sources for the BRST variations) can occur only through cohomologically trivial terms.

hep-th↗
arXiv1994

Self-dual solutions of 2+1 Einstein gravity with a negative cosmological constant

All the causally regular geometries obtained from (2+1)-anti-de Sitter space by identifications by isometries of the form $P \rightarrow (\exp πξ) P$, where $ξ$ is a self-dual Killing vector of $so(2,2)$, are explicitely constructed. Their remarkable properties (Killing vectors, Killing spinors) are listed. These solutions of Einstein gravity with negative cosmological constant are also invariant under the string duality transformation applied to the angular translational symmetry $ϕ\rightarrow ϕ+a$ The analysis is made particularly convenient through the construction of {\em global} coordinates adapted to the identifications.}

hep-th↗
arXiv1994

Local BRST cohomology in the antifield formalism: I. General theorems

We establish general theorems on the cohomology $H^*(s|d)$ of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of local $p$-forms depending on the fields and the antifields (=sources for the BRST variations). It is shown that $H^{-k}(s|d)$ is isomorphic to $H_k(δ|d)$ in negative ghost degree $-k\ (k>0)$, where $δ$ is the Koszul-Tate differential associated with the stationary surface. The cohomological group $H_1(δ|d)$ in form degree $n$ is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether theorem. More generally, the group $H_k(δ|d)$ in form degree $n$ is isomorphic to the space of $n-k$ forms that are closed when the equations of motion hold. The groups $H_k(δ|d)$ $(k>2)$ are shown to vanish for standard irreducible gauge theories. The group $H_2(δ|d)$ is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups $H^{k}(s|d)$ under the introduction of non minimal variables and of auxiliary

hep-th↗
arXiv1994

Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential $s$ modulo the exterior spacetime derivative $d$ for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions $sa+db=0$ depending non trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition $sa+db=0$ besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms.

hep-th↗
arXiv1994

Spacetime locality of the antifield formalism : a "mise au point"

Some general techniques and theorems on the spacetime locality of the antifield formalism are illustrated in the familiar cases of the free scalar field, electromagnetism and Yang-Mills theory. The analysis explicitly shows that recent criticisms of the usual approach to dealing with locality are ill-founded.

hep-th↗
arXiv1993

Renormalization of gauge invariant operators and anomalies in Yang-Mills theory

A long-standing conjecture on the structure of renormalized, gauge invariant, integrated operators of arbitrary dimension in Yang-Mills theory is established. The general solution of the consistency condition for anomalies with sources included is also derived. This is achieved by computing explicitely the cohomology of the full unrestricted BRST operator in the space of local polynomial functionals with ghost number equal to zero or one. The argument does not use power counting and is purely cohomological. It relies crucially on standard properties of the antifield formalism.

hep-th↗
arXiv1993

BRST structure of polynomial Poisson algebras

The BRST structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quadratic Poisson algebras may already be of arbitrarily high rank. Explicit examples are provided, for which the first terms of the BRST generator are given. The calculations are cumbersome but purely algorithmic, and have been treated by means of the computer algebra system REDUCE. Our analysis is classical ($=$ non quantum) throughout.

hep-th↗
arXiv1993

Supersymmetry of the 2+1 black holes

The supersymmetry properties of the asymptotically anti-de Sitter black holes of Einstein theory in 2+1 dimensions are investigated. It is shown that (i) the zero mass black hole has two exact super- symmetries; (ii) extreme $lM=|J|$ black holes with $M \not= 0$ have only one; and (iii) generic black holes do not have any. It is also argued that the zero mass hole is the ground state of (1,1)-adS supergravity with periodic (``Ramond") boundary conditions on the spinor fields.

hep-th↗
arXiv1993

Consistent Interactions between Gauge Fields and Local BRST Cohomology : The Example of Yang-Mills Models

Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the Yang-Mills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the Yang-Mills coupling is therefore rederived through cohomological arguments.

hep-th↗
arXiv1993

Ghosts of ghosts for second class constraints

When one uses the Dirac bracket, second class constraints become first class. Hence, they are amenable to the BRST treatment characteristic of ordinary first class constraints. This observation is the starting point of a recent investigation by Batalin and Tyutin, in which all the constraints are put on the same footing. However, because second class constraints identically vanish as operators in the quantum theory, they are quantum-mechanically reducible and require therefore ghosts of ghosts. Otherwise, the BRST cohomology would not yield the correct physical spectrum. We discuss how to incorporate this feature in the formalism and show that it leads to an infinite tower of ghosts of ghosts. An alternative treatment, in which the brackets of the ghosts are modified, is also mentioned.

hep-th↗