arXiv subjects
Publications and source records attributed to Jorge Zanelli.
The coupling between Chern-Simons theories and matter sources defined by branes of different dimensionalities is examined. It is shown that the standard coupling to membranes, such as the one found in supergravity or in string theory, does not operate in the same way for CS theories; the only p-branes that naturally couple seem to be those with p=2n; these p-branes break the gauge symmetry (and supersymmetry) in a controlled and sensible manner.
The role of Chern-Simons (CS) actions is reviewed, starting from the observation that all classical actions in Hamiltonian form can be viewed as 0+1 CS systems, in the same class with the coupling between the electromagnetic field and a point charge. Some suggestions are derived that could shed some light on the quantization problem in D=2n-1>3 dimensions.
This is intended as a broad introduction to Chern-Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system --with a fiber bundle formulation-- in more than three dimensions, which could provide a firm ground for constructing a quantum theory of the gravitational field. The starting point is a gravitational action which generalizes the Einstein theory for dimensions D>4 --Lovelock gravity. It is then shown that in odd dimensions there is a particular choice of the arbitrary parameters of the action that makes the theory gauge invariant under the (anti-)de Sitter or the Poincare groups. The resulting lagrangian is a Chern-Simons form for a connection of the corresponding gauge groups and the vielbein and the spin connection are parts of this connection field. These theories also admit a natural supersymmetric extension for all odd D where the local supersymmetry algebra closes off-shell and without a need for auxiliary fields. No analogous construction is available in even dimensions. A cursory discussion of the unexpected dynamical features of these theories and a number of open problems are also presented.
Four-dimensional Einstein's General Relativity is shown to arise from a gauge theory for the conformal group, SO(4,2). The theory is constructed from a topological dimensional reduction of the six-dimensional Euler density integrated over a manifold with a four-dimensional topological defect. The resulting action is a four-dimensional theory defined by a gauged Wess-Zumino-Witten term. An ansatz is found which reduces the full set of field equations to those of Einstein's General Relativity. When the same ansatz is replaced in the action, the gauged WZW term reduces to the Einstein-Hilbert action. Furthermore, the unique coupling constant in the action can be shown to take integer values if the fields are allowed to be analytically continued to complex values.
In this paper two things are done. First it is shown how a four dimensional gauged Wess-Zumino-Witten term arises from the five dimensional Einstein-Hilbert plus Gauss-Bonnet lagrangian with a special choice of the coefficients. Second, the way in which the equations of motion of four-dimensional General Relativity arise is exhibited.
An action for a superconformal particle is constructed using the non linear realization method for the group PSU(1,1|2), without introducing superfields. The connection between PSU(1,1|2) and black hole physics is discussed. The lagrangian contains six arbitrary constants and describes a non-BPS superconformal particle. The BPS case is obtained if a precise relation between the constants in the lagrangian is verified, which implies that the action becomes kappa-symmetric.
We review the often forgotten fact that gravitation theories invariant under local de Sitter, anti-de Sitter or Poincare transformations can be constructed in all odd dimensions. These theories belong to the Chern-Simons family and are particular cases of the so-called Lovelock gravities, constructed as the dimensional continuations of the lower dimensional Euler classes. The supersymmetric extensions of these theories exist for the AdS and Poincare groups, and the fields are components of a single connection for the corresponding Lie algebras. In 11 dimensions these supersymmetric theories are gauge theories for the osp(1|32) and the M algebra, respectively. The relation between these new supergravities and the standard theories, as well as some of their dynamical features are also discussed.
Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to deform the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus nonminimally coupled matter. The deformed system is gauge invariant under the Poincare group enlarged by an Abelian ideal. Although the resulting action naively looks like General Relativity plus corrections due to matter sources, it is shown that the nonminimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein-Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions.
We examine anti-de Sitter gravity minimally coupled to a self-interacting scalar field in $D\geq 4$ dimensions when the mass of the scalar field is in the range $m_{\ast}^{2}\leq m^{2}<m_{\ast} ^{2}+l^{-2}$. Here, $l$ is the AdS radius, and $m_{\ast}^{2}$ is the Breitenlohner-Freedman mass. We show that even though the scalar field generically has a slow fall-off at infinity which back reacts on the metric so as to modify its standard asymptotic behavior, one can still formulate asymptotic conditions (i) that are anti-de Sitter invariant; and (ii) that allows the construction of well-defined and finite Hamiltonian generators for all elements of the anti-de Sitter algebra. This requires imposing a functional relationship on the coefficients $a$, $b$ that control the two independent terms in the asymptotic expansion of the scalar field. The anti-de Sitter charges are found to involve a scalar field contribution. Subtleties associated with the self-interactions of the scalar field as well as its gravitational back reaction, not discussed in previous treatments, are explicitly analyzed. In particular, it is shown that the fields develop extra logarithmic branches for specific values of the scalar field mass (in addition to the known logarithmic branch at the B-F bound).
Some dynamical aspects of five-dimensional supergravity as a Chern-Simons theory for the SU(2,2|N) group, are analyzed. The gravitational sector is described by the Einstein-Hilbert action with negative cosmological constant and a Gauss-Bonnet term with a fixed coupling. The interaction between matter and gravity is characterized by intricate couplings which give rise to dynamical features not present in standard theories. Depending on the location in phase space, the dynamics can possess different number of propagating degrees of freedom, including purely topological sectors. This inhomogeneity of phase space requires special care in the analysis. Background solutions in the canonical sectors, which have regular dynamics with maximal number of degrees of freedom, are shown to exist. Within this class, explicit solutions given by locally AdS spacetimes with nontrivial gauge fields are constructed, and BPS states are identified. It is shown that the charge algebra acquires a central extension due to the presence of the matter fields. The Bogomol'nyi bound for these charges is discussed. Special attention is devoted to the N=4 case since then the gauge group has a U(1) central charge and the phase space possesses additional irregular sectors.
A nontrivial scalar field configuration of vanishing energy-momentum is reported. These matter configurations have no influence on the metric and therefore they are not be "detected" gravitationally. This phenomenon occurs for a time-dependent nonminimally coupled and self-interacting scalar field on the 2+1 (BTZ) black hole geometry. We conclude that such stealth configurations exist for the static 2+1 black hole for any value of the nonminimal coupling parameter $ζ\neq0$ with a fixed self-interaction potential $U_ζ(Φ)$. For the range $0<ζ\leq1/2$ potentials are bounded from below and for the range $0<ζ<1/4$ the stealth field falls into the black hole and is swallowed by it at an exponential rate, without any consequence for the black hole.
A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem.
It is shown that flat spacetime can be dressed with a real scalar field that satisfies the nonlinear Klein-Gordon equation without curving spacetime. Surprisingly, this possibility arises from the nonminimal coupling of the scalar field with the curvature, since a footprint of the coupling remains in the energy-momentum tensor even when gravity is switched off. Requiring the existence of solutions with vanishing energy-momentum tensor fixes the self-interaction potential as a local function of the scalar field depending on two coupling constants. The solutions describe shock waves and, in the Euclidean continuation, instanton configurations in any dimension. As a consequence of this effect, the tachyonic solutions of the free massive Klein-Gordon equation become part of the vacuum.
The dynamics of five-dimensional Chern-Simons theories is analyzed. These theories are characterized by intricate self couplings which give rise to dynamical features not present in standard theories. As a consequence, Dirac's canonical formalism cannot be directly applied due to the presence of degeneracies of the symplectic form and irregularities of the constraints on some surfaces of phase space, obscuring the dynamical content of these theories. Here we identify conditions that define sectors where the canonical formalism can be applied for a class of non-Abelian Chern-Simons theories, including supergravity. A family of solutions satisfying the canonical requirements is explicitly found. The splitting between first and second class constraints is performed around these backgrounds, allowing the construction of the charge algebra, including its central extension.
The eleven-dimensional gravitational action invariant under local Poincare transformations is given by the dimensional continuation of the Euler class of ten dimensions. Here we show that the supersymmetric extension of this action leads, through the Noether procedure, to a theory with the local symmetry group given by the M-algebra. The fields of the theory are the vielbein, the Lorentz (spin) connection, one gravitino, and two 1-forms which transform as second and fifth rank antisymmetric Lorentz tensors. These fields are components of a single connection for the M-algebra and the supersymmetric Lagrangian can be seen to be a Chern-Simons form. The dynamics has a multiplicity of degenerate vacua without propagating degrees of freedom. The theory is shown to admit solutions of the form S^{10-d} x X_{d+1}, where X_{d+1} is a warped product of R with a d-dimensional spacetime. Among this class, the gravitational effective action describes a propagating graviton only if d=4 and the spacetime has positive cosmological constant. The perturbations around this solution reproduce linearized General Relativity around four-dimensional de Sitter spacetime.
Here we consider a gravitational action having local Poincare invariance which is given by the dimensional continuation of the Euler density in ten dimensions. It is shown that the local supersymmetric extension of this action requires the algebra to be the maximal extension of the N=1 super-Poincare algebra. The resulting action is shown to describe a gauge theory for the M-algebra, and is not the eleven-dimensional supergravity theory of Cremmer-Julia-Scherk. The theory admits a class of vacuum solutions of the form S^{10-d} x Y_{d+1}, where Y_{d+1} is a warped product of R with a d-dimensional spacetime. It is shown that a nontrivial propagator for the graviton exists only for d=4 and positive cosmological constant. Perturbations of the metric around this solution reproduce linearized General Relativity around four-dimensional de Sitter spacetime.
We consider a self-interacting scalar field whose mass saturates the Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a negative cosmological constant in D \geq 3 dimensions. It is shown that the asymptotic behavior of the metric has a slower fall-off than that of pure gravity with a localized distribution of matter, due to the back-reaction of the scalar field, which has a logarithmic branch decreasing as r^{-(D-1)/2} ln r for large radius r. We find the asymptotic conditions on the fields which are invariant under the same symmetry group as pure gravity with negative cosmological constant (conformal group in D-1 dimensions). The generators of the asymptotic symmetries are finite even when the logarithmic branch is considered but acquire, however, a contribution from the scalar field.
An exact four-dimensional black hole solution of gravity with a minimally coupled self-interacting scalar field is reported. The event horizon is a surface of negative constant curvature enclosing the curvature singularity at the origin, and the scalar field is regular everywhere outside the origin. This solution is an asymptotically locally AdS spacetime. The strong energy condition is satisfied on and outside the event horizon. The thermodynamical analysis shows the existence of a critical temperature, below which a black hole in vacuum undergoes a spontaneous dressing up with a nontrivial scalar field in a process reminiscent of ferromagnetism.