We investigate the effects of the leading tadpole potentials of 10D tachyon-free non-supersymmetr... more We investigate the effects of the leading tadpole potentials of 10D tachyon-free non-supersymmetric strings in warped products of flat geometries of the typeMp+1× R × T10−p−2depending on a single coordinate. In the absence of fluxes and forp <8, there are two families of these vacua for the orientifold disk-level potential, both involving a finite internal interval. Their asymptotics are surprisingly captured by tadpole-free solutions, isotropic for one family and anisotropic at one end for the other. In contrast, for the heterotic torus-level potential there are four types of vacua. Their asymptotics are always tadpole-dependent and isotropic at one end lying at a finite distance, while at the other end, which can lie at a finite or infinite distance, they can be tadpole-dependent isotropic or tadpole-free anisotropic. We then elaborate on the general setup for including symmetric fluxes, and present the three families of exact solutions that emerge when the orientifold potentia...
We review the main results of our investigations motivated by the tadpole potentials of ten-dimen... more We review the main results of our investigations motivated by the tadpole potentials of ten-dimensional strings with broken supersymmetry. While these are at best partial indications, it is hard to resist the feeling that they do capture some lessons of String Theory. For example, these very tadpole potentials lead to weak-string-coupling cosmologies that appear to provide clues on the onset of the inflation from an initial fast roll. The transition, if accessible to us, would offer a natural explanation for the lack of power manifested by the CMB at large angular scales. In addition, the same tadpole potentials can drive spontaneous compactifications to lower-dimensional Minkowski spaces at corresponding length scales. Furthermore, the cosmological solutions exhibit an intriguing "instability of isotropy" that, if taken at face value, would point to an accidental origin of compactification. Finally, symmetric static AdS × S solutions driven by the tadpole potentials also exist, but they are unstable due to mixings induced by their internal fluxes. On the other hand, the original Dudas-Mourad solution is perturbatively stable, and we have gathered some detailed evidence that instabilities induced by internal fluxes can be held under control in a similar class of weak-coupling type-I IB compactifications to Minkowski space.
We study the perturbative stability of four settings that arise in String Theory, when dilaton po... more We study the perturbative stability of four settings that arise in String Theory, when dilaton potentials accompany the breaking of Supersymmetry, in the tachyon-free USp(32) and U(32) orientifold models, and also in the heterotic SO(16) × SO(16) model. The first two settings are a family ofAdS3×S7vacua of the orientifold models and a family ofAdS7×S3vacua of the heterotic model, supported by form fluxes, with small world-sheet and string-loop corrections within wide ranges of parameters. In both cases we find some unstable scalar perturbations, as a result of mixings induced by fluxes, confirming for the first class of vacua a previous result. However, in the second class of vacua they only affect theℓ= 1 modes, so that a ℤ2projection induced by an overall parity in the internal space suffices to eliminate them, leading to perturbative stability. Moreover, the constant dilaton profiles of these vacua allow one to extend the analysis to generic potentials, thus exploring the possibl...
We describe how unbounded three-form fluxes can lead to families of AdS 3 × S 7 vacua, with const... more We describe how unbounded three-form fluxes can lead to families of AdS 3 × S 7 vacua, with constant dilaton profiles, in the U Sp(32) model with "brane supersymmetry breaking" and in the U (32) 0'B model, if their (projective-)disk dilaton tadpoles are taken into account. We also describe how, in the SO(16) × SO(16) heterotic model, if the torus vacuum energy Λ is taken into account, unbounded seven-form fluxes can support similar AdS 7 × S 3 vacua, while unbounded three-form fluxes, when combined with internal gauge fields, can support AdS 3 × S 7 vacua, which continue to be available even if Λ is neglected. In addition, special gauge field fluxes can support, in the SO(16) × SO(16) heterotic model, a set of AdS n × S 10−n vacua, for all n = 2, .., 8. String loop and α ′ corrections appear under control when large form fluxes are allowed.
We consider, in a string theory framework, physical processes of phenomenological interest in mod... more We consider, in a string theory framework, physical processes of phenomenological interest in models with a low string scale. The amplitudes we study involve treelevel virtual gravitational exchange, divergent in a field-theoretical treatment, and massive gravitons emission, which are the main signatures of this class of models. First, we discuss the regularization of summations appearing in virtual gravitational (closed string) Kaluza-Klein exchanges in Type I strings. We argue that a convenient manifestly ultraviolet convergent low energy limit of type I string theory is given by an effective field theory with an arbitrary cutoff Λ in the closed (gravitational) channel and a related cutoff M 2 s /Λ in the open (Yang-Mills) channel. We find the leading string corrections to the field theory results. Second, we calculate exactly string tree-level three and four-point amplitudes with gauge bosons and one massive graviton and examine string deviations from the field-theory result.
A geometrical construction of superconformal transformations in six dimensional (2,0) superspace ... more A geometrical construction of superconformal transformations in six dimensional (2,0) superspace is proposed. Superconformal Killing vectors are determined. It is shown that the transformation of the tensor multiplet involves a zero curvature non-trivial cochain.
We show that there is only one operator having some minimal properties enabling it to be a one ph... more We show that there is only one operator having some minimal properties enabling it to be a one photon position operator. These properties are stated, and the solution is shown to be the photon position operator proposed by Pryce. This operator has non-commuting components. Nevertheless, it is shown that one can find states localized with an arbitrary precision.
International Journal of Theoretical Physics, 2005
We review how one can construct a deconstructed gravity by a transverse latticification of 5D Gen... more We review how one can construct a deconstructed gravity by a transverse latticification of 5D General Relativity. The obtained theory is a multigravity theory, with link fields that are explicitly constructed out of the metric. We also discuss the spectrum of the theory at the level of the linearized theory.
A modification of Kaluza–Klein theory is proposed which is general enough to admit an arbitrary f... more A modification of Kaluza–Klein theory is proposed which is general enough to admit an arbitrary finite noncommutative internal geometry. It is shown that the existence of a nontrivial extension to the total geometry of a linear connection on space–time places severe restrictions on the structure of the noncommutative factor. A counter-example is given.
We address some general issues related to torsion and Noether currents for Fermi fields in the pr... more We address some general issues related to torsion and Noether currents for Fermi fields in the presence of boundaries, with emphasis on the conditions that guarantee charge conservation. We also describe exact solutions of these boundary conditions and some implications for string vacua with broken supersymmetry.
The commutative algebra of functions on a manifold is extended to a noncommutative algebra by con... more The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of n×n complex matrices. Noncommutative geometry is used to formulate an extension of the Einstein-Hilbert action. The result is shown to be equivalent to the usual Kaluza-Klein theory with the manifold SUn as an internal space, in a truncated approximation.
It has been shown that the massless irreducible representations of the Poincaré group with contin... more 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.
A classical action is proposed which upon quantisation yields massless particles belonging to the... more A classical action is proposed which upon quantisation yields massless particles belonging to the continuous spin representation of the Poincar\'e 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.
We show that the Wigner equations describing the continuous spin representations can be obtained ... more 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.
The tachyon-free nonsupersymmetric string theories in ten dimensions have dilaton tadpoles which ... more The tachyon-free nonsupersymmetric string theories in ten dimensions have dilaton tadpoles which forbid a Minkowski vacuum. We determine the maximally symmetric backgrounds for the U Sp(32) Type I string and the SO(16) × SO(16) heterotic string. The static solutions exhibit nine dimensional Poincaré symmetry and have finite 9D Planck and Yang-Mills constants. The low energy geometry is given by a ten dimensional manifold with two boundaries separated by a finite distance which suggests a spontaneous compactification of the ten dimensional string theory.
Twisted Coalgebra Structure of Poincar´ e Group and Noncommutative QFT on the Moyal Space
We study the consequences of twisting the coalgebra structure of Poincare group in a quantum fiel... more We study the consequences of twisting the coalgebra structure of Poincare group in a quantum field theory on a flat space-time. First, we construct a tensor product representation 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.
We investigate maximally symmetric backgrounds in nonsupersymmetric string vacua with D-branes an... more 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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Papers by J. Mourad