arXiv subjects

J. Mourad

Publications and source records attributed to J. Mourad.

At least 37 records · Page 2Linked to original sources

arXiv2008

Three Dimensional Quantum Geometry and Deformed Poincare Symmetry

We study a three dimensional non-commutative space emerging in the context of three dimensional Euclidean quantum gravity. Our starting point is the assumption that the isometry group is deformed to the Drinfeld double D(SU(2)). We generalize to the deformed case the construction of the flat Euclidean space as the quotient of its isometry group ISU(2) by SU(2). We show that the algebra of functions becomes the non-commutative algebra of SU(2) distributions endowed with the convolution product. This construction gives the action of ISU(2) on the algebra and allows the determination of plane waves and coordinate functions. In particular, we show that: (i) plane waves have bounded momenta; (ii) to a given momentum are associated several SU(2) elements leading to an effective description of an element in the algebra in terms of several physical scalar fields; (iii) their product leads to a deformed addition rule of momenta consistent with the bound on the spectrum. We generalize to the non-commutative setting the local action for a scalar field. Finally, we obtain, using harmonic analysis, another useful description of the algebra as the direct sum of the algebra of matrices. The algebra of matrices inherits the action of ISU(2): rotations leave the order of the matrices invariant whereas translations change the order in a way we explicitly determine.

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arXiv2008

(A)dS exchanges and partially-massless higher spins

We determine the current exchange amplitudes for free totally symmetric tensor fields $\vf_{μ_1 ... μ_s}$ of mass $M$ in a $d$-dimensional $dS$ space, extending the results previously obtained for $s=2$ by other authors. Our construction is based on an unconstrained formulation where both the higher-spin gauge fields and the corresponding gauge parameters $Λ_{μ_1 >... μ_{s-1}}$ are not subject to Fronsdal's trace constraints, but compensator fields $α_{μ_1 ... μ_{s-3}}$ are introduced for $s > 2$. The free massive $dS$ equations can be fully determined by a radial dimensional reduction from a $(d+1)$-dimensional Minkowski space time, and lead for all spins to relatively handy closed-form expressions for the exchange amplitudes, where the external currents are conserved, both in $d$ and in $(d+1)$ dimensions, but are otherwise arbitrary. As for $s=2$, these amplitudes are rational functions of $(ML)^2$, where $L$ is the $dS$ radius. In general they are related to the hypergeometric functions $_3F_2(a,b,c;d,e;z)$, and their poles identify a subset of the "partially-massless" discrete states, selected by the condition that the gauge transformations of the corresponding fields contain some non-derivative terms. Corresponding results for $AdS$ spaces can be obtained from these by a formal analytic continuation, while the massless limit is smooth, with no van Dam-Veltman-Zakharov discontinuity.

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arXiv2007

Group theoretical approach to quantum fields in de Sitter space II. The complementary and discrete series

We use an algebraic approach based on representations of de Sitter group to construct covariant quantum fields in arbitrary dimensions. We study the complementary and the discrete series which correspond to light and massless fields and which lead new feature with respect to the massive principal series we previously studied (hep-th/0606119). When considering the complementary series, we make use of a non-trivial scalar product in order to get local expressions in the position representation. Based on these, we construct a family of covariant canonical fields parametrized by SU(1,1)/U(1). Each of these correspond to the dS invariant alpha-vacua. The behavior of the modes at asymptotic times brings another difficulty as it is incompatible with the usual definition of the in and out vacua. We propose a generalized notion of these vacua which reduces to the usual conformal vacuum in the conformally massless limit. When considering the massless discrete series we find that no covariant field obeys the canonical commutation relations. To further analyze this singular case, we consider the massless limit of the complementary scalar fields we previously found. We obtain canonical fields with a deformed representation by zero modes. The zero modes have a dS invariant vacuum with singular norm. We propose a regularization by a compactification of the scalar field and a dS invariant definition of the vertex operators. The resulting two-point functions are dS invariant and have a universal logarithmic infrared divergence.

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arXiv2007

Metastable Vacua in Brane Worlds

We analyze vacuum decay in brane world setups, where a free scalar field in five dimensions has a localized potential admitting metastable vacua. We study in particular the bounce solution and its properties in flat and warped spaces. In the latter case, placing into a deeply warped region the term in the potential that lifts the vacuum degeneracy, can increase indefinitely the lifetime of the false vacuum. We discuss the application to metastable vacua in supersymmetric brane-world constructions.

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arXiv2007

QFT with Twisted Poincaré Invariance and the Moyal Product

We study the consequences of twisting the Poincare invariance in a quantum field theory. First, we construct a Fock space compatible with the twisting and the corresponding creation and annihilation operators. Then, we show that a covariant field linear in creation and annihilation operators does not exist. Relaxing the linearity condition, a covariant field can be determined. We show that it is related to the untwisted field by a unitary transformation and the resulting n-point functions coincide with the untwisted ones. We also show that invariance under the twisted symmetry can be realized using the covariant field with the usual product or by a non-covariant field with a Moyal product. The resulting S-matrix elements are shown to coincide with the untwisted ones up to a momenta dependent phase.

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arXiv2007

Current Exchanges and Unconstrained Higher Spins

The (Fang-)Fronsdal formulation for free fully symmetric (spinor-) tensors rests on (gamma-)trace constraints on gauge fields and parameters. When these are relaxed, glimpses of the underlying geometry emerge: the field equations extend to non-local expressions involving the higher-spin curvatures, and with only a pair of additional fields an equivalent ``minimal'' local formulation is also possible. In this paper we complete the discussion of the ``minimal'' formulation for fully symmetric (spinor-) tensors, constructing one-parameter families of Lagrangians and extending them to (A)dS backgrounds. We then turn on external currents, that in this setting are subject to conventional conservation laws and, by a close scrutiny of current exchanges in the various formulations, we clarify the precise link between the local and non-local versions of the theory. To this end, we first show the equivalence of the constrained and unconstrained local formulations, and then identify a unique set of non-local Lagrangian equations which behave in exactly the same fashion in current exchanges.

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arXiv2006

Group theoretical approach to quantum fields in de Sitter space I. The principal series

Using unitary irreducible representations of the de Sitter group, we construct the Fock space of a massive free scalar field. In this approach, the vacuum is the unique dS invariant state. The quantum field is a posteriori defined by an operator subject to covariant transformations under the dS isometry group. This insures that it obeys canonical commutation relations, up to an overall factor which should not vanish as it fixes the value of hbar. However, contrary to what is obtained for the Poincare group, the covariance condition leaves an arbitrariness in the definition of the field. This arbitrariness allows to recover the amplitudes governing spontaneous pair creation processes, as well as the class of alpha vacua obtained in the usual field theoretical approach. The two approaches can be formally related by introducing a squeezing operator which acts on the state in the field theoretical description and on the operator in the present treatment. The choice of the different dS invariant schemes (different alpha vacua) is here posed in very simple terms: it is related to a first order differential equation which is singular on the horizon and whose general solution is therefore characterized by the amplitude on either side of the horizon. Our algebraic approach offers a new method to define quantum field theory on some deformations of dS space.

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arXiv2005

The continuous spin limit of higher spin field equations

We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the spin to infinity with their product being fixed. The result allows to transform the Wigner equations to a gauge invariant Fronsdal-like form. We also give the generalisation of the Wigner equations to higher dimensions with fields belonging to arbitrary representations of the massless little group.

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arXiv2005

Continuous spin and tensionless strings

A classical action is proposed which upon quantisation yields massless particles belonging to the continuous spin representation of the Poincaré group. The string generalisation of the action is identical to the tensionless extrinsic curvature action proposed by Savvidy. We show that the BRST quantisation of the string action gives a critical dimension of 28. The constraints result in a number of degrees of freedom which is the same as the bosonic string.

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arXiv2005

Continuous spin particles from a string theory

It has been shown that the massless irreducible representations of the Poincaré group with continuous spin can be obtained from a classical point particle action which admits a generalization to a conformally invariant string action. The continuous spin string action is quantized in the BRST formalism. We show that the vacuum carries a continuous spin representation of the Poincaré group and that the spectrum is ghost-free.

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arXiv2004

Solutions of multigravity theories and discretized brane worlds

We determine solutions to 5D Einstein gravity with a discrete fifth dimension. The properties of the solutions depend on the discretization scheme we use and some of them have no continuum counterpart. In particular, we find that the neglect of the lapse field (along the discretized direction) gives rise to Randall-Sundrum type metric with a negative tension brane. However, no brane source is required. We show that this result is robust under changes in the discretization scheme. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We find however one particular scheme which leads to an undetermined lapse reflecting the reparametrization invariance of the continuum theory. We also find other solutions, with no continuum counterpart with changes in the metric signature or avoidance of singularity. We show that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales. We also discuss some cosmological solutions.

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arXiv2003

Multigravity from a discrete extra dimension

Multigravity theories are constructed from the discretization of the extra dimension of five dimensional gravity. Using an ADM decomposition, the discretization is performed while maintaining the four dimensional diffeomorphism invariance on each site. We relate the Goldstone bosons used to realize nonlinearly general covariance in discretized gravity to the shift fields of the higher dimensional metric. We investigate the scalar excitations of the resulting theory and show the absence of ghosts and massive modes; this is due to a local symmetry inherited from the reparametrization invariance along the fifth dimension.

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arXiv2003

On Tachyon kinks from the DBI action

We consider solitonic solutions of the DBI tachyon effective action for a non-BPS brane in the presence of an electric field. We find that for a constant electric field $\tilde E\le 1$, regular solitons compactified on a circle admit a singular and decompactified limit corresponding to Sen's proposal provided the tachyon potential satisfies some restrictions. On the other hand for the critical electric field $\tilde E=1$, regular and finite energy solitons are constructed without any restriction on the potential.

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arXiv2003

On cosmologically induced hierarchies in string theory

We propose, within a perturbative string theory example, a cosmological way to generate a large hierarchy between the observed Planck mass and the fundamental string scale. Time evolution results in three large space dimensions, one additional dimension transverse to our world and five small internal dimensions with a very slow time evolution. The evolution of the string coupling and internal space generate a large Planck mass. However due to an exact compensation between the time evolution of the internal space and that of the string coupling, the gauge and Yukawa couplings on our Universe are time independent.

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arXiv2003

Tachyon kinks on non BPS D-branes

We consider solitonic solutions of the DBI tachyon effective action for a non-BPS brane. When wrapped on a circle, these solutions are regular and have a finite energy. We show that in the decompactified limit, these solitons give Sen's infinitely thin finite energy kink -- interpreted as a BPS brane -- provided that some conditions on the potential hold. In particular, if for large $T$ the potential is exponential, $V = e^{-T^a}$, then Sen's solution is only found for $a<1$. For power-law potentials $V = 1/T^b$, one must have $b>1$. If these conditions are not satisfied, we show that the lowest energy configuration is the unstable tachyon vacuum with no kinks. We examine the stability of the solitons and the spectrum of small perturbations.

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arXiv2002

Time and space dependent backgrounds from nonsupersymmetric strings

We investigate maximally symmetric backgrounds in nonsupersymmetric string vacua with D-branes and O-planes localized in the compact space. We find a class of solutions with a perturbative string coupling constant in all regions of spacetime. Depending on the particular model, we find either a time evolution with a big-bang type singularity or a space dependent background with generically orbifold singularities. We show that the result can be interpreted as a supersymmetric bulk with some symmetries broken by the boundaries. We also discuss an interesting connection to Lorentzian and Euclidian orbifolds.

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arXiv2002

Orientifolds of String Theory Melvin backgrounds

We study the dynamics of type I strings on Melvin backgrounds, with a single or multiple twisted two-planes. We construct two inequivalent types of orientifold models that correspond to (non-compact) irrational versions of Scherk-Schwarz type breaking of supersymmetry. In the first class of vacua, D-branes and O-planes are no longer localized in space-time but are smeared along the compact Melvin coordinate with a characteristic profile. On the other hand, the second class of orientifolds involves O-planes and D-branes that are both rotated by an angle proportional to the twist. In case of ``multiple Melvin spaces'', some amount of supersymmetry is recovered if the planes are twisted appropriately and part of the original O-planes are transmuted into new ones. The corresponding boundary and crosscap states are determined.

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arXiv2001

Charged and Uncharged D-branes in various String Theories

We describe how the D-brane spectra of the various ten-dimensional string theories can be related to general properties of the open-closed duality, encoded in the $S$ and $P$ matrices of the conformal field theory. We also complete the classification and the description of non-BPS branes in these string theories, elucidating their non-Abelian structures and the nature of the corresponding super-Higgs mechanisms. We find that the type 0 theories and their orientifolds have two types of uncharged branes, distinguished by their couplings to the closed string tachyon. We also find that the 0A orientifold has the unusual feature of having charged and uncharged branes with identical world-volume dimensions. We conclude with some comments on fractional branes, elucidating their role in connection with the boundary states of $D_{odd}$ SU(2) WZW models.

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