arXiv subjects

Jorge Zanelli

Publications and source records attributed to Jorge Zanelli.

At least 55 records · Page 3Linked to original sources

arXiv2014

Local supersymmetry without SUSY partners

A gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz algebras, and that could describe the low energy particle phenomenology is constructed. These two symmetries are connected by fermionic supercharges. The system includes an internal gauge connection 1-form $A$, a spin-1/2 Dirac spinor $ψ$, the Lorentz connection $ω$, and the vielbein $e$. The connection one-form is in the adjoint representation of G, while $ψ$ is in the fundamental. In contrast to standard supergravity, the metric is not a fundamental field and is in the center of the superalgebra: it is not only invariant under the internal gauge group and under Lorentz transformations, but is also invariant under supersymmetry. The features of this theory that mark the difference with standard supersymmetry are: A) The number of fermionic and bosonic states is not necessarily the same; B) There are no superpartners with equal mass, "bosoninos", sleptons and squarks are absent; C) Although this supersymmetry originates in a local gauge theory and gravity is included, there is no gravitino; D) Fermions acquire mass from their coupling to the background or from self-couplings, while bosons remain massless. In odd dimensions, the Chern-Simons form provides an action that is quasi-invariant under the entire superalgebra. In even dimensions, the Yang-Mills form $ < F *F>$ is the only natural option, and the symmetry breaks down to [G x SO(1,D-1)]. In 4D, the construction follows the Townsend - Mac Dowell-Mansouri approach. Due to the absence of osp(4|2)-invariant traces in four dimensions, the resulting Lagrangian is only invariant under [U(1) x SO(3,1)], and includes a Nambu--Jona-Lasinio term. In this case, the Lagrangian depends on a single dimensionful parameter that fixes Newton's constant, the cosmological constant and the NJL coupling.

hep-th↗

arXiv2014

Black hole solutions in Chern-Simons AdS supergravity

We study charged AdS black hole solutions in five-dimensional Chern-Simons supergravity. The minimal supergroup containing such AdSxU(1) configurations is the superunitary group SU(2,2|N). For this model, we find analytic black hole solutions that asymptote to locally AdS spacetime at the boundary. A solution can carry U(1) charge provided the spacetime torsion is non-vanishing. Thus, we analyze the most general configuration consistent with the local AdS isometries in Riemann-Cartan space. The coupling of torsion in the action resembles that of the universal axion of string theory, and it is ultimately due to this field that the theory acquires propagating degrees of freedom. Through a careful analysis of the canonical structure the local degrees of freedom of the theory are identified in the static symmetric sector of phase space.

hep-th↗

arXiv2014

Gribov ambiguity and degenerate systems

The relation between Gribov ambiguity and degeneracies in the symplectic structure of physical systems is analyzed. It is shown that, in finite-dimensional systems, the presence of Gribov ambiguities in regular constrained systems (those where the constraints are functionally independent) always leads to a degenerate symplectic structure upon Dirac reduction. The implications for the Gribov-Zwanziger approach to QCD are discussed.

hep-th↗

arXiv2014

The BTZ black hole as a Lorentz-flat geometry

It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.

gr-qc↗

arXiv2013

Cosmology with Scalar-Euler form Coupling

A coupling between the spacetime geometry and a scalar field involving the Euler four-form can have important consequences in General Relativity. The coupling is a four-dimensional version of the Jackiw-Teitelboim action, in which a scalar couples to the Euler two-form in two dimensions. In this case the first order formalism, in which the vierbein (or the metric) and the spin connection (or the afine connection) are varied independently, is not equivalent to the second order one, in which the geometry is completely determined by the metric. This is because the torsion postulate (T=0) is not valid and one cannot algebraically solve the spin connection from its own field equation. The direct consequence of this obstruction is that the torsion becomes a new source for the metric curvature, and even if the scalar field is very slowly varying over cosmic scales as to have no observable astronomical efects at the galactic scale, it has important dynamical efects that can give rise to a cosmological evolution radically diferent from the standard FRWL model.

gr-qc↗

arXiv2012

Chern-Simons Forms in Gravitation Theories

The Chern-Simons (CS) form evolved from an obstruction in mathematics into an important object in theoretical physics. In fact, the presence of CS terms in physics is more common than one may think: they seem to play an important role in high Tc superconductivity and in recently discovered topological insulators. In classical physics, the minimal coupling in electromagnetism and to the action for a mechanical system in Hamiltonian form are examples of CS functionals. CS forms are also the natural generalization of the minimal coupling between the electromagnetic field and a point charge when the source is not point-like but an extended fundamental object, a membrane. They are found in relation with anomalies in quantum field theories, and as Lagrangians for gauge fields, including gravity and supergravity. A cursory review of the role of CS forms in gravitation theories is presented at an introductory level.

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arXiv2012

Gribov copies, BRST-exactness and Chern-Simons theory

The path integral approach for a 3D Chern-Simons theory is discussed with a focus on the question of metric independence and BRST-exactness in the light of Gribov ambiguity. Copies of the vacuum satisfying the strong boundary conditions and with trivial winding number are shown to exist. This problem is relevant for Yang-Mills theory in 2+1 dimensions as well. Furthermore, it is also shown that there are regular background metrics supporting an infinite number of zero modes of the Abelian Faddeev-Popov operator in the Coulomb gauge. In order to avoid overcounting one could restrict the possible metrics which enter in the gauge fixing but this would imply that, at a quantum level, three-dimensional Chern-Simons theories do depend on the metric.

hep-th↗

arXiv2012

Reflections on Cosmology: an Outsider's Point of View

Some of the assumptions of cosmology, as based on the simplest version of General Relativity, are discussed. It is argued that by slight modifications of standard gravitation theory, our notion of the sources of gravity {the right hand side of Einstein's equations{, could be something radically different from what is usually expected. One example is exhibited to prove the point, and some consequences are discussed.

gr-qc↗

arXiv2012

Supersymmetry of a different kind

A local supersymmetric action for a (2+1)-dimensional system including gravity, the electromagnetic field and a Dirac spin-1/2 field is presented. The action is a Chern-Simons form for a connection of the OSp(2|2) group. All the fields enter as parts of the connection, that transforms in the adjoint representation of the gauge group. The system is off-shell invariant under local (gauge) supersymmetry. Although the supersymmetry is locally realized, there is no spin-3/2 gravitino, and is therefore not supergravity. The fields do not necessarily form supersymmetric doublets of equal mass, and moreover, the fermion may acquire mass through the coupling with the background geometry, while the bosons --the U(1) field and the spin connection-- remain massless.

hep-th↗

arXiv2012

Quantum Degenerate Systems

Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems --in which the degeneracy cannot be eliminated by redefining variables in the action--, the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.

hep-th↗

arXiv2012

Optical Properties of a θ-Vacuum

Chern-Simons (CS) forms generalize the minimal coupling between gauge potentials and point charges, to sources represented by charged extended objects (branes). The simplest example of such a CS-brane coupling is a domain wall coupled to the electromagnetic CS three-form. This describes a topologically charged interface where the CS form AdA is supported, separating two three-dimensional spatial regions in 3+1 spacetime. Electrodynamics at either side of the brane is described by the same Maxwell's equations, but those two regions have different vacua, characterized by a different value of the θ-parameter multiplying the Pontryagin form F ^ F. The θ-term is the abelian version of the concept introduced by 't Hooft for the resolution of the U(1) problem in QCD. We point out that CS-generalized classical electrodynamics shows new phenomena when two neighboring regions with different θ-vacua are present. These topological effects result from surface effects induced by the boundary and we explore the consequences of such boundary effects for the propagation of the electromagnetic field in Maxwell theory. Several features, including optical and electrostatic/magnetostatic responses, which may be observable in condensed matter systems, like topological insulators, are discussed.

hep-th↗

arXiv2011

Theta term in a bounded region

We analyse the physical implications of adding a topological density term $θTr(F\wedge F)$ to a gauge theory in a bounded region. In particular, we calculate the Casimir effect on a spherical region and we show that the result is not periodic in $θ$, contrary to what would be expected for a true topological density. The topological nature of the $θ$-term can be restored if an additional boundary term required by the Atiyah-Patodi-Singer theorem is included. Then, the periodicity is trivially restored because the resulting Casimir energy is independent of $θ$. The results of the present work suggest that the observable effects of the $θ$-term could be very small even without assuming $θ$ itself to be small.

hep-th↗

arXiv2011

Geometry and stability of spinning branes in AdS gravity

The geometry of spinning codimension-two branes in AdS spacetime is analyzed in three and higher dimensions. The construction of non-extremal solutions is based on identifications in the covering of AdS space by isometries that have fixed points. The discussion focuses on the cases where the parameters of spinning states can be related to the velocity of a boosted static codimension-two brane. The resulting configuration describes a single spinning brane, or a set of intersecting branes, each one produced by an independent identification. The nature of the singularity is also examined, establishing that the AdS curvature acquires one in the form of a Dirac delta distribution. The stability of the branes is studied in the framework of Chern-Simons AdS supergravity. A class of branes, characterized by one free parameter, are shown to be stable when the BPS conditions are satisfied. In 3D, these stable branes are extremal, while in higher dimensions, the BPS branes are not the extremal ones.

hep-th↗

arXiv2010

Naked Singularities, Topological Defects and Brane Couplings

A conical defect in (2+1) anti-de Sitter space is a BTZ solution with a negative mass parameter. This is a naked singularity, but a rather harmless one: it is a point particle. Naturally, the energy density and the spacetime curvature have a delta-like singularity at the apex of the conical defect, but that doesn't give rise to any unphysical situations. Since the conical solution implies the presence of a source, applying reverse enginnering, one can identify the coupling term that is required in the action to account for that source. In that way, a relation is established between the identification operation that gives rise to the topological defect and the interaction term in the action that produces it. This idea has a natural extension to higher dimensions, where instead of a point particle (zero-brane) one finds membranes of even spatial dimensions (p-branes, with p=2n). The generalization to other abelian and nonabelian gauge theories --including (super-) gravities-- is fairly straightforward: the 2n-brane couple to a (2n+1) Chern-Simons form. The construction suggests a generic role for Chern-Simons forms as the natural way to couple a gauge connection to a brane and avoids the inconsistency that results from the minimal coupling between a brane and a fundamental p-form field.

hep-th↗

arXiv2010

Stable p-branes in Chern-Simons AdS supergravities

We construct static codimension-two branes in any odd dimension D, with negative cosmological constant, and show that they are exact solutions of Chern-Simons (super)gravity theory for (super)AdS coupled to external sources. The stability of these solutions is analyzed by counting the number of preserved supersymmetries. It is shown that static massive (D-3)-branes are unstable unless some suitable gauge fields are added and the brane is extremal. In particular, in three dimensions, a 0-brane is recognized as the negative mass counterpart of the BTZ black hole. For these 0-branes, we write explicitly electromagnetically charged BPS states with various number of preserved supersymmetries within the OSp(p|2) x OSp(q|2) supergroups. In five dimensions, we prove that stable 2-branes with electromagnetic charge always exist for the generic supergroup SU(2,2|N), where N is different than 4. For the special case N=4, in which the CS supergravity requires the addition of a nontrivial gauge field configuration in order to preserve maximal number of degrees of freedom, we show for two different static 2-branes that they are BPS states (one of which is the ground state), and from the corresponding algebra of charges we show that the energy is bounded from below. In higher dimensions, our results admit a straightforward generalization, although there are presumably more solutions corresponding to different intersections of the elementary objects.

hep-th↗

arXiv2009

Couplings between Chern-Simons gravities and 2p-branes

The interaction between Chern-Simons (CS) theories and localized external sources (2p-branes) is analyzed. This interaction generalizes the minimal coupling between a point charge (0-brane) and a gauge connection. The external currents that define the 2p-branes are covariantly constant (D-2p-1)-forms coupled to (2p-1) CS forms. The general expression for the sources --charged with respect to the corresponding gauge algebra-- is presented, focusing on two special cases: 0-branes and (D-3)-branes. In any dimension, 0-branes are constructed as topological defects produced by a surface deficit of (D-2)-sphere in AdS space, and they are not constant curvature spaces for D>3. They correspond to dimensionally continued black holes with negative mass. On the other hand, in the case of CS (super) gravities, the (D-3)-branes are naked conical singularities (topological defects) obtained by identification of points with a Killing vector. In 2+1 dimensions, extremal spinning branes of this type are BPS states. Stable (D-3)-branes are shown to exist also in higher dimensions, as well. Classical field equations are also discussed and in the presence of sources there is a large number of inequivalent and disconnected sectors in solution space.

hep-th↗

arXiv2009

On the negative spectrum of the 2+1 black hole

In (2+1)-dimensional gravity with negative cosmological constant, the states in the negative energy range, between AdS (M=-1) and the so-called BTZ black hole ($M\geq 0$), correspond to topological defects with angular deficit $0<α<2π$. These defects are produced by (static or spinning) 0-branes which, in the extreme case $M\ell =-|J|$, admit globally-defined covariantly constant spinors. Thus, these branes correspond to BPS solitons and are stable ground state candidates for the corresponding supersymmetric extension of 2+1 AdS gravity. These branes constitute external currents that couple in a gauge-invariant way to three-dimensional AdS gravity.

hep-th↗

arXiv2008

Chern-Simons foam

Chern-Simons theory can be defined on a cell complex, such as a network of bubbles, which is not a (Hausdorff) manifold. Requiring gauge invariance determines the action, including interaction terms at the intersections, and imposes a relation between the coupling constants of the CS terms on adjacent cell walls. We also find simple conservation laws for charges at the intersections.

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