Model building by coset space dimensional reduction in ten-dimensions with direct product gauge symmetry

We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and gauge group is a direct product of two Lie groups. We list up candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space,we find fermion and scalar representations of $G_{\mathrm{GUT}} \times U(1)$ with $G_{\mathrm{GUT}}=SU(5), SO(10)$ and $E_6$ which accomodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with a different dimension for $G_{\mathrm{GUT}}=SO(10)$ and $E_6$ models.Comment: 14 pages; added local report number, added refferenc

Scalar Kaluza-Klein modes in a multiply warped braneworld

The Kaluza-Klein (KK) modes of a massive scalar field on a 3-brane embedded in six dimensional multiply warped spacetime are determined. Due to the presence of warping along both the extra dimensions the KK mass spectrum splits into two closely spaced branches which is a distinct feature of this model compared to the five dimensional Randall-Sundrum model. This new cluster of the KK mode spectrum is expected to have interesting phenomenological implications for the upcoming collider experiments. Such a scenario may also be extended for even larger number of orbifolded extra dimensions.Comment: 10 pages, Revte

Inflation in Multidimensional Quantum Cosmology

We extend to multidimensional cosmology Vilenkin's prescription of tunnelling from nothing for the quantum origin of the observable Universe. Our model consists of a $D+4$-dimensional spacetime of topology ${\cal R}\times {\cal S}^3 \times{\cal S}^D$, with a scalar field (``chaotic inflaton'') for the matter component. Einstein gravity and Casimir compactification are assumed. The resulting minisuperspace is 3--dimensional. Patchwise we find an approximate analytic solution of the Wheeler--DeWitt equation through which we discuss the tunnelling picture and the probability of nucleation of the classical Universe with compactifying extra dimensions. Our conclusion is that the most likely initial conditions, although they do not lead to the compactification of the internal space, still yield (power-law) inflation for the outer space. The scenario is physically acceptable because the inner space growth is limited to $\sim 10^{11}$ in 100 e-foldings of inflation, starting from the Planck scale.Comment: RevTeX, 30 pages, 4 figures available via fax on request to [email protected], submitted to Phys. Rev.

Compactification, Vacuum Energy and Quintessence

We study the possibility that the vacuum energy density of scalar and internal-space gauge fields arising from the process of dimensional reduction of higher dimensional gravity theories plays the role of quintessence. We show that, for the multidimensional Einstein-Yang-Mills system compactified on a $R \times S^3 \times S^d$ topology, there are classically stable solutions such that the observed accelerated expansion of the Universe at present can be accounted for without upsetting structure formation scenarios or violating observational bounds on the vacuum energy density.Comment: 15 pages, Latex, Third Award in 1999 Essay Competition of the Gravity Research Foundatio

Matter-gravity interaction in a multiply warped braneworld,

The role of a bulk graviton in predicting the signature of extra dimensions through collider-based experiments is explored in the context of a multiply warped spacetime. In particular it is shown that in a doubly warped braneworld model, the presence of the sixth dimension, results in enhanced concentration of graviton Kaluza Klein (KK) modes compared to that obtained in the usual 5-dimensional Randall-Sundrum model. Also, the couplings of these massive graviton KK modes with the matter fields on the visible brane turn out to be appreciably larger than that in the corresponding 5- dimensional model. The significance of these results are discussed in the context of KK graviton search at the Large Hadron Collider (LHC).Comment: 13 pages, 2 table

Scalar kinks and fermion localisation in warped spacetimes

Scalar kinks propagating along the bulk in warped spacetimes provide a thick brane realisation of the braneworld. We consider here, a class of such exact solutions of the full Einstein-scalar system with a sine-Gordon potential and a negative cosmological constant. In the background of the kink and the corresponding warped geometry, we discuss the issue of localisation of spin half fermions (with emphasis on massive ones) on the brane in the presence of different types of kink-fermion Yukawa couplings. We analyse the possibility of quasi-bound states for large values of the Yukawa coupling parameter $\gamma_F$ (with $\nu$, the warp factor parameter kept fixed) using appropriate, recently developed, approximation methods. In particular, the spectrum of the low--lying states and their lifetimes are obtained, with the latter being exponentially enhanced for large $\nu \gamma_F$. Our results indicate quantitatively, within this model, that it is possible to tune the nature of warping and the strength and form of the Yukawa interaction to obtain trapped massive fermion states on the brane, which, however, do have a finite (but very small) probability of escaping into the bulk.Comment: 22 pages, 4 figures, RevTex

Finite SU(N)^k Unification

We consider N=1 supersymmetric gauge theories based on the group SU(N)_1 x SU(N)_2 x ... x SU(N)_k with matter content (N,N*,1,...,1) + (1,N,N*,...,1) + >... + (N*,1,1,...,N) as candidates for the unification symmetry of all particles. In particular we examine to which extent such theories can become finite and we find that a necessary condition is that there should be exactly three families. We discuss further some phenomenological issues related to the cases (N,k) = (3,3), (3,4), and (4,3), in an attempt to choose those theories that can become also realistic. Thus we are naturally led to consider the SU(3)^3 model which we first promote to an all-loop finite theory and then we study its additional predictions concerning the top quark mass, Higgs mass and supersymmetric spectrum.Comment: 15 page

Gravitational excitons from extra dimensions

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces near minima of an effective potential have a form of massive scalar fields in the external space-time. Parameters of models which ensure minima of the effective potentials are obtained for particular cases and masses of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20 pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97

Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this expansion applied to the Wilson-Polchinski equation in the case of the $N$-vector model with the symmetry $\mathrm{O}(N)$. As a test, the critical exponents $$ and $\nu$ as well as the subcritical exponent $\omega$ (and higher ones) are estimated in three dimensions for values of $N$ ranging from 1 to 20. I compare the results with the corresponding estimates obtained in preceding studies or treatments of other $\mathrm{O}(N)$ exact RG equations at second order. The possibility of varying $N$ allows to size up the derivative expansion method. The values obtained from the resummation of high orders of perturbative field theory are used as standards to illustrate the eventual convergence in each case. A peculiar attention is drawn on the preservation (or not) of the reparametrisation invariance.Comment: Dedicated to Lothar Sch\"afer on the occasion of his 60th birthday. Final versio

High orders of perturbation theory: are renormalons significant?

According to Lipatov, the high orders of perturbation theory are determined by saddle-point configurations (instantons) of the corresponding functional integrals. According to t'Hooft, some individual large diagrams, renormalons, are also significant and they are not contained in the Lipatov contribution. The history of the conception of renormalons is presented, and the arguments in favor of and against their significance are discussed. The analytic properties of the Borel transforms of functional integrals, Green functions, vertex parts, and scaling functions are investigated in the case of \phi^4 theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou - Zinn-Justin hypothesis) is proved. It rules out the existence of the renormalon singularities pointed out by t'Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of \phi^4 theory.Comment: 28 pages, 8 figures include