Searcharxiv⌕ Search

arXiv subjects

Victor O. Rivelles

Publications and source records attributed to Victor O. Rivelles.

At least 37 records · Page 2Linked to original sources
arXiv2008

Aspects of Noncommutative Scalar/Tensor Duality

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U(1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in $θ$. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order $θ$ is also derived.

hep-th↗
arXiv2006

Noncommutative Gravity

We consider simple extensions of noncommutativity from flat to curved spacetime. One possibility is to have a generalization of the Moyal product with a covariantly constant noncommutative tensor $θ^{μν}$. In this case the spacetime symmetry is restricted to volume preserving diffeomorphisms which also preserve $θ^{μν}$. Another possibility is an extension of the Kontsevich product to curved spacetime. In both cases the noncommutative product is nonassociative. We find the the order $θ^2$ noncommutative correction to the Newtonian potential in the case of a covariantly constant $θ^{μν}$. It is still of the form $1/r$ plus an angle dependent piece. The coupling to matter gives rise to a propagator which is $θ$ dependent.

hep-th↗
arXiv2006

Duality in Noncommutative Maxwell-Chern-Simons Theory

Applying a master action technique we obtain the dual of the noncommutative Maxwell-Chern-Simons theory. The equivalence between the Maxwell-Chern-Simons theory and the self-dual model in commutative space-time does not survive in the non-commutative setting. We also point out an ambiguity in the Seiberg-Witten map.

hep-th↗
arXiv2006

Dispersion Relations in Noncommutative Theories

We present a detailed study of plane waves in noncommutative abelian gauge theories. The dispersion relation is deformed from its usual form whenever a constant background electromagnetic field is present and is similar to that of an anisotropic medium with no Faraday rotation nor birefringence. When the noncommutativity is induced by the Moyal product we find that for some values of the background magnetic field no plane waves are allowed when time is noncommutative. In the Seiberg-Witten context no restriction is found. We also derive the energy-momentum tensor in the Seiberg-Witten case. We show that the generalized Poynting vector obtained from the energy-momentum tensor, the group velocity and the wave vector all point in different directions. In the absence of a constant electromagnetic background we find that the superposition of plane waves is allowed in the Moyal case if the momenta are parallel or satisfy a sort of quantization condition. We also discuss the relation between the solutions found in the Seiberg-Witten and Moyal cases showing that they are not equivalent.

hep-th↗
arXiv2005

Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual

We consider the Maxwell-Chern-Simons theory in noncommutative three dimensional space-time. We show that the Seiberg-Witten map is ambiguous due to the dimensional coupling constant. To get the dual theory we start from a master action obtained by promoting the global shift invariance to a local one. We also obtain the mapping between the observables of the two equivalent theories. We show that the equivalence between the Maxwell-Chern-Simons theory and the self-dual model in commutative space-time does not survive in the non-commutative setting.

hep-th↗
arXiv2004

Noncommutative Theories, Seiberg-Witten Map and Gravity

We review the connection between noncommutative field theories and gravity. When the noncommutativity is induced by the Moyal product we can use the Seiberg-Witten map in order to deal with ordinary fields. We then show that the effect of the noncommutativity is the same as a field dependent gravitational background. The gravitational background is that of a gravitational plane wave and the coupling is charge dependent. Uncharged fields couple more strongly than the charged ones. Deviations from the usual dispersion relations are discussed and we show that they are also charge dependent.

hep-th↗
arXiv2003

Triviality of Higher Derivative Theories

We show that some higher derivative theories have a BRST symmetry. This symmetry is due to the higher derivative structure and is not associated to any gauge invariance. If physical states are defined as those in the BRST cohomology then the only physical state is the vacuum. All negative norm states, characteristic of higher derivative theories, are removed from the physical sector. As a consequence, unitarity is recovered but the S-matrix is trivial. We show that a class of higher derivative quantum gravity theories have this BRST symmetry so that they are consistent as quantum field theories. Furthermore, this BRST symmetry may be present in both relativistic and non-relativistic systems.

hep-th↗
arXiv2003

Noncommutative Field Theories and Gravity

We show that after the Seiberg-Witten map is performed the action for noncommutative field theories can be regarded as a coupling to a field dependent gravitational background. This gravitational background depends only on the gauge field. Charged and uncharged fields couple to different backgrounds and we find that uncharged fields couple more strongly than the charged ones. We also show that the background is that of a gravitational plane wave. A massless particle in this background has a velocity which differs from the velocity of light and we find that the deviation is larger in the uncharged case. This shows that noncommutative field theories can be seen as ordinary theories in a gravitational background produced by the gauge field with a charge dependent gravitational coupling.

hep-th↗
arXiv2003

Quantization in Ads and the Ads/CFT Correspondence

The quantization of a scalar field in AdS leads to two kinds of normalizable modes, usually called regular and irregular modes. The regular one is easily taken into account in the standard prescription for the AdS/CFT correspondence. The irregular mode requires a modified prescription which we argue is not completely satisfactory. We discuss an alternative quantization in AdS which incorporates boundary terms in a natural way. Within this quantization scheme we present an improved prescription for the AdS/CFT correspondence which can be applied to both, regular and irregular modes. Boundary conditions other than Dirichlet are naturally treated in this new improved setting.

hep-th↗
arXiv2002

The low energy limit of the non-commutative Wess-Zumino model

The non-commutative Wess-Zumino model is used as a prototype for studying the low energy behaviour of a renormalizable non-commutative field theory. We start by deriving the potential mediating the fermion-fermion and boson-boson interactions in the non-relativistic regime. The quantum counterparts of these potentials are afflicted by irdering ambiguities but we show that there exists an ordering prescription which makes them hermitean. For space/space noncommutativity it turns out that Majorana fermions may be pictured as rods oriented perpendicularly to the direction of motion showing a lack of localituy, while bosons remain insensitive to the effects of noncommutativity. For time/space noncommutativity bosopns and fermions can be regarded as rods oriented along the direction of motion. For both cases of noncommutativity the scattering state described scattered waves, with at least one wave having negative time delay signalizing the underlying nonlocality. The superfield formulation of the model is used to compute the corresponding effective action in the one- and two-loop approximations. In the case of time/space noncommutativity, unitarity is violated in the relativistic regime. However, this does not preclude the existence of the unitary low energy limit.

hep-th↗
arXiv2002

On New Forms of the BRST Transformations

We show how to derive systematically new forms of the BRST transformations for a generic gauge fixed action. They arise after a symmetry of the gauge fixed action is found in the sector involving the Lagrange multiplier and its canonical momentum.

hep-th↗
arXiv2002

Off-Shell Duality in Maxwell and Born-Infeld Theories

It is well known that the classical equations of motion of Maxwell and Born-Infeld theories are invariant under a duality symmetry acting on the field strengths. We review the implementation of the SL(2,Z) duality in these theories as linear but non-local transformations of the potentials.

hep-th↗
arXiv2001

Energy and the AdS/CFT Correspondence

We consider a scalar field theory on AdS in both minimally and non-minimally coupled cases. We show that there exist constraints which arise in the quantization of the scalar field theory on AdS which cannot be reproduced through the usual AdS/CFT prescription. We argue that the usual energy, defined through the stress-energy tensor, is not the natural one to be considered in the context of the AdS/CFT correspondence. We analyze a new definition of the energy which makes use of the Noether current corresponding to time displacements in global coordinates. We compute the new energy for Dirichlet, Neumann and mixed boundary conditions on the scalar field and for both the minimally and non-minimally coupled cases. Then, we perform the quantization of the scalar field theory on AdS showing that, for `regular' and `irregular' modes, the new energy is conserved, positive and finite. We show that the quantization gives rise, in a natural way, to a generalized AdS/CFT prescription which maps to the boundary all the information contained in the bulk. In particular, we show that the divergent local terms of the on-shell action contain information about the Legendre transformed generating functional, and that the new constraints for which the irregular modes propagate in the bulk are the same constraints for which such divergent local terms cancel out. In this situation, the addition of counterterms is not required. We also show that there exist particular cases for which the unitarity bound is reached, and the conformal dimension becomes independent of the effective mass. This phenomenon has no bulk counterpart.

hep-th↗
arXiv2001

Off-Shell Duality in Born-Infeld Theory

The classical equations of motion of Maxwell and Born-Infeld theories are known to be invariant under a duality symmetry acting on the field strengths. We implement the SL(2,Z) duality in these theories as linear but non-local transformations on the potentials. We show that the action and the partition function in the Hamiltonian formalism are modular invariant in any gauge. For the Born-Infeld theory we find that the longitudinal part of the fields have to be complexified.

hep-th↗
arXiv2001

Noncommutative Supersymmetric Field Theories

We discuss some properties of noncommutative supersymmetric field theories which do not involve gauge fields. We concentrate on the renormalizability issue of these theories.

hep-th↗
arXiv2000

Gauge Dependence in the AdS/CFT Correspondence

We consider the AdS space formulation of the classical dynamics deriving from the Stueckelberg Lagrangian. The on-shell action is shown to be free of infrared singularities as the vector boson mass tends to zero. In this limit the model becomes Maxwell theory formulated in an arbitrary covariant gauge. Then we use the AdS/CFT correspondence to compute the two-point correlation functions on the boundary. It is shown that the gauge dependence concentrates on the contact terms.

hep-th↗