Compact Spatial Dimension Research Articles

Application of Kaluza–Klein theory in modelling compact stars: exploring extra dimensions

ABSTRACT A theoretical framework for calculating the mass–radius curve of compact stars in the Kaluza–Klein space–time is introduced, with one additional compact spatial dimension. Static, spherically symmetric solutions are considered, with the equation of state provided by a zero temperature, interacting multidimensional Fermi gas. To model the strong force between baryons, a repulsive potential is introduced, which is linear in the particle number density. The maximal mass of compact stars is calculated for different model parameters, and with a physical parameter choice, it satisfies observational data, meaning that it is possible to model simple, realistic objects within this framework. Based on this comparison, a limiting size for the observational regime of extra dimensions in compact stars is provided, with $r_\mathrm{c} \gtrsim 0.2$ fm.

On aether terms in a space-time with a compact extra dimension

In this paper, we explicitly calculate the aether-like corrections for the electromagnetic field in the case when the space-time involves an extra compact spatial dimension besides of usual four dimensions. Our methodology is based on an explicit summation over the Kaluza–Klein tower of fields which turns out to be no more difficult than the finite-temperature calculations. We found some new terms which can be treated as certain five-dimensional generalizations of the aether-like terms kappa ^{mnpq}F_{mn}F_{pq} and bar{psi }c^{mn}gamma _mpartial _n psi which in four dimensions are treated as important ingredients of the Lorentz-breaking extension of the standard model. We have shown that these new terms become to dominate in the limit where the extra dimension is very small, allowing us to suggest that there will be essential modifications of quantum corrections if our space indeed has a small extra spatial dimension. Moreover, we have shown that in the CPT-even case we have extra new particles as a consequence of the extra dimension.

Revisiting vacuum energy in compact spacetimes

We revisit the calculation of vacuum energy density in compact spacetimes. For the general case of k compact spatial dimensions in p+k dimensional Minkowski spacetime, we calculate the Casimir force on a piston placed in the presence of external electromagnetic fields. We observe that while the presence of a strong external magnetic field reduces the intensity of the Casimir force, the presence of an electric field enhances it instead. We discuss various physical cases and also derive the particle production rate in the presence of such external fields in compact spacetimes. We observe that the pair production rate is enhanced in the presence of a piston.

Notes on massless scalar field partition functions, modular invariance and Eisenstein series

The partition function of a massless scalar field on a Euclidean spacetime manifold ℝd−1 × \U0001d54b2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝp × \U0001d54bq+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On \U0001d54bd+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

Geodesic Circular Orbits Sharing the Same Orbital Frequencies in the Black String Spacetime

We consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with Ωr^, Ωφ^, and Ωω^ in a particular region of parameter space around black string spacetime geometry. We study the effect of a compact extra spatial dimension on the isofrequency pairing of geodesic orbits and show that such orbits would occur in the allowed region when particles move along the black string. We find that the presence of the compact extra dimension leads to an increase in the number of the isofrequency pairing of geodesic orbits. Interestingly we also find that isofrequency pairing of geodesic orbits in the region of parameter space cannot be realized beyond the critical value Jcr≈0.096 of the conserved quantity of the motion arising from the compact extra spatial dimension.

Inquiring the Unruh–DeWitt detector about the global property of spacetime

We investigate the effect of spatial compactification on the transition rate of an inertial or accelerated Unruh–Dewitt detector coupled to an untwisted or twisted massless quantum scalar field. Four typical cases of the detector’s motion in the compactified Minkowski spacetime are considered respectively. Our results indicate that the detector’s transition rates are crucially dependent on the spatial compactification length, the magnitude and direction of detector’s velocity, the detector’s acceleration, and the field structure. As these factors change, the detector’s spontaneous emission and absorption processes can be enhanced or weakened at different degrees. In particular, when the compact length is small, the behavior of transition rate in the case of the twisted field is quite distinct from that of the untwisted field. Notably, when the detector moves at a constant velocity with nonzero components along the compact and non-compact directions, our study finds that the spontaneous emission rate depends on the component of velocity along the non-compact direction besides that along the compact direction. This is in sharp contrast with the case of the free Minkowski spacetime. Moreover, for the uniformly accelerated detector along the non-compact direction, the spatial compactification clearly modifies both the spontaneous emission and absorption rates, as the modifying factors depend on the compact length and the detector’s acceleration. Our work indirectly but comprehensively examines the nonequivalence of inertial frames in the compactified Minkowski spacetime, and meanwhile provides a theoretical way to identify the orientation and the size of the compact spatial dimension.

Proof of dispersion relations for the amplitude in theories with a compactified space dimension

The analyticity properties of the scattering amplitude in the nonforward direction are investigated for a field theory in the manifold R3,1 ⨂ S1. The theory is obtained from a massive, neutral scalar field theory of mass m0 defined in flat five dimensional spacetime upon compactification on a circle, S1. The resulting theory is endowed with a massive scalar field which has the lowest mass, m0, as of the original five dimensional theory and a tower of massive Kaluza-Klein states. We derive nonforward dispersion relations for scattering of the excited Kaluza-Klein states in the Lehmann-Symanzik-Zimmermann formulation of the theory. In order to accomplish this object, first we generalize the Jost-Lehmann-Dyson theorem for a relativistic field theory with a compact spatial dimension. Next, we show the existence of the Lehmann-Martin ellipse inside which the partial wave expansion converges. The scattering amplitude satisfies fixed-t dispersion relations when |t| lies within the Lehmann-Martin ellipse.

Energy nonconservation as a link between f(R,T) gravity and noncommutative quantum theory

$f(R,T)$ gravity was proposed as an extension of the $f(R)$ theories, containing not just geometrical correction terms to the General Relativity equations, but also material correction terms, dependent on the trace of the energy-momentum tensor $T$. These material extra terms prevent the energy-momentum tensor of the theory to be conserved, even in a flat background. Energy nonconservation is a prediction of quantum theory with time-space noncommutativity. If time is considered as an operator and there are compact spatial coordinates which do not commute with time, then the time evolution gets quantized and energy conservation can be violated. In the present work we construct a model in a 5-dimensional flat spacetime consisting of 3 commutative spatial dimensions and 1 compact spatial dimension whose coordinate does not commute with time. We show that energy flows from the 3-dimensional commutative slice into the compact extra dimension (and vice-versa), so that conservation of energy is restored. In this model the energy flux is proportional to the energy density of the matter content, leading to a differential equation for $f(R,T)$, thus providing a physical criterion to restrict the functional form of $f(R,T)$. We solve this equation and analyze the behavior of its solution in a spherically symmetric context.

Virtual and thermal Schwinger processes

Electric flux may be screened by pair nucleation of heavy charges, a process that has a simple description in terms of a worldline instanton. When flux is wrapped around a small compact spatial dimension, worldline instantons still induce flux dissipation, but the leading process does not create real charged pairs. Instead, dissipation can be described in effective field theory as the production of long-wavelength scalar quanta via parametric resonance. The rate is computed semiclassically, and comments are made on the related problem of pair creation at finite temperature, for which differing results appear in the literature. Flux dissipation and the weak gravity conjecture together imply that the proper distance in field space a homogeneous axion field can traverse is bounded.

Induced Cosmological Constant in Brane Models with a Compact Dimension

The vacuum expectation value of the surface energy-momentum tensor of a charged scalar field on a flat brane in an anti-de Sitter space-time with a compact spatial dimension is studied. The existence of a constant gauge field is also assumed. Because of the nontrivial topology of the space, the latter leads to an Aharonov-Bohm type effect. A generalized zeta-function method is used for renormalizing the vacuum expectation value. The cosmological constant induced on the brane is a periodic function of the magnetic flux through the compact dimension and, depending on the parameters of the problem, can be either positive or negative.

Boosted Kaluza–Klein magnetic monopole

We consider a Kaluza–Klein vacuum solution which is closely related to the Gross–Perry–Sorkin (GPS) magnetic monopole. The solution can be obtained from the Euclidean Taub–NUT solution with an extra compact fifth spatial dimension within the formalism of Kaluza–Klein reduction. We study its physical properties as appearing in (3+1) spacetime dimensions, which turns out to be a static magnetic monopole. We then boost the GPS magnetic monopole along the extra dimension, and perform the Kaluza–Klein reduction. The resulting four-dimensional spacetime is a rotating stationary system, with both electric and magnetic fields. In fact, after the boost the magnetic monopole turns into a string connected to a dyon.

Induced Cosmological Constant in Braneworlds with Compact Dimensions

We investigate the cosmological constant induced by quantum fluctuations of a bulk charged scalar field on a brane in background of locally anti-de Sitter spacetime with toroidally compact spatial dimensions. Along compact dimension quasiperiodicity conditions are imposed with general phases and, in addition, the presence of a constant gauge field is assumed. The latter gives rise to Aharonov-Bohm type effect on the characteristics of the scalar vacuum. The renormalization of the vacuum energy density on the brane is done by making use of the generalized zeta function technique. The behavior of the cosmological constant is studied as a function of the location of the brane, of the length of the compact dimensions and of the magnetic flux enclosed by the compact dimension. In particular, it is shown that the cosmological constant is a periodic function of the magnetic flux with the period equal to the flux quantum.

Vacuum densities for a charged scalar field in de Sitter space-time with compact dimensions

The vacuum expectation value of the energy-momentum tensor is investigated for a charged scalar field in dS space-time with toroidally compact spatial dimensions in the presence of a classical constant gauge field. Due to the nontrivial topology, the latter gives rise to an Aharonov-Bohm-like effect on the vacuum characteristics. The vacuum energy density and stresses are even periodic functions of the magnetic flux enclosed by the compact dimensions. For small values of the comoving lengths of the compact dimensions as compared with the dS curvature radius, the effects of gravity on the topological contributions are small, and the expectation values are expressed in terms of the corresponding quantities in the Minkowski bulk by the standard conformal relation. For large values of the comoving lengths, depending on the field mass, two regimes are realized with monotonic and oscillatory damping of the expectation values. We show that the sign of the the vacuum energy density can be controlled by tuning the magnetic flux enclosed by the compact dimensions.

Four boosted tops from a Regge gluon

The hierarchy problem can by addressed by extending the four-dimensional space-time to include an extra compact spatial dimension with non-trivial “warped” metric, as first suggested by Randall and Sundrum. If the Randall-Sundrum framework is realized in string theory, and if the Standard Model particles propagate in the extra dimension, Regge excitations of the Standard Model states should appear around the TeV scale. In a previous publication, we proposed a field-theoretic framework to model the tensor (spin-2) Regge partner of the gluon. Here, we use this framework to study the collider phenomenology of this particle. We find that Regge gluon decays involving Kaluza-Klein (KK) partners of Standard Model fields are very important. In particular, the decay to two KK gluons (with one possibly off-shell) dominates in most of the parameter space. This decay produces a very distinctive experimental signature: four highly boosted top quarks. We present a preliminary study of the detection prospects for this signal at the Large Hadron Collider (LHC). We find that Regge gluon masses up to about 2 TeV can be probed with 10 fb−1 of data at 7 TeV center-of-mass energy. With design luminosity at 14 TeV, the LHC should be sensitive to Regge gluon masses up to at least 3.5 TeV.

Tensor Reggeons from warped space at the LHC

The hierarchy problem can be addressed by extending the four-dimen\-sional space-time to include an extra compact spatial dimension with non-trivial ``warped metric, as first suggested by Randall and Sundrum. If the Randall-Sundrum framework is realized in string theory, the effective value of the string scale in the vicinity of the infrared boundary should be in the TeV domain. The most attractive models of this type embed the Standard Model particles as zero-modes of five-dimensional fields. In such models, Regge excitations of the Standard Model states should appear around the TeV scale. We construct a toy model that describes tensor (spin-2) excitations of the Standard Model gauge bosons, and their on-shell couplings with light matter and gauge fields, within this framework. We use this toy model to predict the phenomenologically important features of the tensor Regge gluon, such as its mass, production cross section at the LHC, and decay patterns.

Search for Extra Dimensions with the CMS Detector

Multidimensional theories at TeV energies, as given in the brane world scenarios with large or compact extra spatial dimensions (ED), are discussed. One interesting feature of recent ED models is the rich low-energy phenomenology that originates from the Kaluza-Klein spectrum of various particles propagating in ED. A series of searches is addressed in the CMS experiment with different signatures.

QCD with one compact spatial dimension

The realization of global symmetries can depend on the geometry of the underlying space. In particular, compactification can lead to spontaneous breaking of such symmetries. Four-dimensional QCD with fundamental representation fermions embedded in a space with one compact spatial dimension has a critical length, at which the theory undergoes a phase transition and develops a ground state that is no longer charge conjugation invariant. We show this behavior with simulations of three color, four flavor QCD. We use unrooted staggered fermion at two values of the lattice spacing and several quark masses. We discuss the dependence of the transition on the dynamical fermion mass as well as its connection to the finite temperature and chiral phase transitions.

Higher-dimensional Kaluza–Klein monopoles

It is well known that the Kaluza–Klein monopole of Sorkin, Gross and Perry can be obtained from the Euclidean Taub–NUT solution with an extra compact fifth spatial dimension via Kaluza–Klein reduction. In this paper we consider Taub–NUT-like solutions of the vacuum Einstein field equations, with or without cosmological constant, in five dimensions and higher, and similarly perform Kaluza–Klein reductions to obtain new magnetic KK brane solutions in higher dimensions, as well as further sphere reductions to magnetic monopoles in four dimensions. In six dimensions we also employ spatial and timelike Hopf dualities to untwist the circle fibration characteristic to these spaces and obtain charged strings. A variation of these methods in ten dimensions leads to a non-uniform electric string in five dimensions.

Proton Lifetime from SU(5) Unification in Extra Dimensions

We provide detailed estimates of the proton lifetime in the context of simple supersymmetric SU(5) grand unified models with an extra compact spatial dimension, described by the orbifold S/(Z_2 x Z_2') and by a large compactification scale Mc. We focus on a class of models where the grand unified symmetry is broken by the compactification mechanism and where baryon violation proceeds mainly through gauge vector boson exchange so that the proton lifetime scales as the fourth power of Mc. We carefully compute Mc from a next-to-leading analysis of gauge coupling unification and we find that Mc can only be predicted up to an overall factor one hundred. The simplest model, where the dominant decay mode is (pi^0 e+) and has no flavour suppression, is strongly constrained by existing data, but not totally ruled out. We also analyze models where some of the matter fields are localized in the extra space and proton decay is flavour suppressed. In models associated to anarchy in the neutrino sector the preferred decay channel is (K+ {\bar \nu}) and the lifetime can be within the reach of the next generation of experiments.

Formation of domain wall lattices

We study the formation of domain walls in a phase transition in which an ${S}_{5}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry is spontaneously broken to ${S}_{3}\ifmmode\times\else\texttimes\fi{}{S}_{2}.$ In one compact spatial dimension we observe the formation of a stable domain wall lattice. In two spatial dimensions we find that the walls form a network with junctions, there being six walls to every junction. The network of domain walls evolves so that junctions annihilate antijunctions. The final state of the evolution depends on the relative dimensions of the simulation domain. In particular we never observe the formation of a stable lattice of domain walls for the case of a square domain but we do observe a lattice if one dimension is somewhat smaller than the other. During the evolution, the total wall length in the network decays with time as ${t}^{\ensuremath{-}0.71},$ as opposed to the usual ${t}^{\ensuremath{-}1}$ scaling typical of regular ${Z}_{2}$ networks.