Higher-dimensional Theories Research Articles

Cosmological brane systems in warped spacetime

In this paper, we discuss the time-dependent brane solutions in higher-dimensional supergravity theories. We particularly focus on the dynamical extensions of the intersecting brane solutions involving three branes. We also show that in the near-horizon limits, where the time dependence is negligible, these branes describe warped anti--de Sitter spacetimes as in the corresponding static solutions. We finally examine the lower-dimensional cosmological dynamics obtained after compactifications of the higher-dimensional solutions and show the solutions we have found give the four-dimensional universe with power-law expansion.

An alternative model of spherical oscillator

An alternative model of Higgs spherical oscillator is considered. The quasiradial wave functions and energy spectra of the alternative model of spherical oscillator on the D-dimensional sphere and D-dimensional two-sheeted hyperboloid are found. It is shown that the energy spectrum of the alternative model of spherical oscillator on the two-sheeted hyperboloid takes both discrete and continuous values. The obtained results can be applied for constructing quantum Hall effect theory in higher dimensions.

Oxidation ofD=3cosets and Bonnor dualities inD≤6

Bonnor's map in General Relativity is duality between (dimensionally reduced) vacuum gravity and static truncation of electro-vacuum theory. It was used as a tool to generate an exact solution of electro-vacuum from some vacuum solution. It can be expected that similar dualities will be useful for solution generation in higher-dimensional theories too. Here we study such maps within a class of theories in dimensions $D\leq 6$ using oxidation of D=3 cosets and consistent truncation of the corresponding theories. Our class includes those theories whose D=3 symmetries are subgroups of $G=O(5,4)$. It contains six-dimensional minimal supergravity, five-dimensional minimal and $U(1)^3$ supergravities and a number of four-dimensional theories which attracted attention recently in the search of exact solutions. We give explicit reduction/truncation formulas relating different theories in dimensions $D=4, 5, 6$ in terms of metrics and matter fields and discuss various alternative duality chains between them.

Higher dimensional abelian Chern-Simons theories and their link invariants

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions 4l + 3, whose parameter k is quantized. The generalized Wilson (2l + 1)-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of (2l + 1)-loops, first on closed (4l + 3)-manifolds through a novel geometric computation, then on \documentclass[12pt]{minimal}\begin{document}$\mathbb {R}^{4l+3}$\end{document}R4l+3 through an unconventional field theoretic computation.

Radion inflation in higher-dimensional gravity theory

We study a radion model for inflation and density perturbation identifying the scalar field arising from the five-dimensional gravity on $M_4 x S^1$ with the inflaton. The inflaton potential arising from 5D graviton and matter one-loop effects is shown to possess the desirable slow-roll property. This radion model contains only a small number of parameters and there is an ample parameter region which reproduces (without fine-tuning) all precision astrophysical data.

Inflationary dynamics with a non-Abelian gauge field

We study the dynamics of the universe with a scalar field and an SU(2) non-Abelian Gauge (Yang-Mills) field. The scalar field has an exponential potential and the Yang-Mills field is coupled to the scalar field with an exponential function of the scalar field. We find that the magnetic component of the Yang-Mills field assists acceleration of the cosmic expansion and a power-law inflation becomes possible even if the scalar field potential is steep, which may be expected from some compactification of higher-dimensional unified theories of fundamental interactions. This power-law inflationary solution is a stable attractor in a certain range of coupling parameters. Unlike the case with multiple Abelian gauge fields, the power-law inflationary solution with the dominant electric component is unstable because of the existence of non-linear coupling of the Yang-Mills field. We also analyze the dynamics for the non-inflationary regime, and find several attractor solutions.

Particle production and dissipation caused by the Kaluza-Klein tower

Two-step dissipation is studied in supersymmetric models in which the field in motion couples to bulk fields in the higher dimensional space. Since the Kaluza-Klein tower of the intermediate field changes its mass-spectrum during the evolution, there could be back-reaction from the tower. Then the system may eventually cause significant dissipation of the kinetic energy if the tower is coupled to light fields in the thermal bath. To see what happens in the higher dimensional theory, we consider three models for the scenario, which are carefully prepared. In these models the extension is obvious but it does not disturb the original set-ups. The third model suggests that the evolution of the volume moduli may feel significant friction from the Kaluza-Klein tower.

On Higher Dimensional Kaluza-Klein Theories

We present a new method for the study of general higher dimensional Kaluza-Klein theories. Our new approach is based on the Riemannian adapted connection and on a theory of adapted tensor fields in the ambient space. We obtain, in a covariant form, the fully general 4D equations of motion in a (4 +n)D general gauge Kaluza-Klein space. This enables us to classify the geodesics of the (4 +n)D space and to show that the induced motions in the 4D space bring more information than motions from both the 4D general relativity and the 4D Lorentz force equations. Finally, we note that all the previous studies on higher dimensional Kaluza-Klein theories are particular cases of the general case considered in the present paper.

How have global shocks impacted the real effective exchange rates of individual euro area countries since the euro’s creation?

This paper uncovers the response pattern to global shocks of euro area countries’ real effective exchange rates before and after the start of Economic and Monetary Union (EMU), a largely open ended question when the euro was created. We apply to that end a newly developed methodology based on high dimensional VAR theory. This approach features a dominant unit to a large set of over 60 countries’ real effective exchange rates and is based on the comparison of two estimated systems: one before and one after EMU. We find strong evidence that the pattern of responses depends crucially on the nature of global shocks. In particular, post-EMU responses to global US dollar shocks have become similar to Germany’s response before EMU, i.e., to that of the economy that used to issue Europe’s most credible legacy currency. By contrast, post-EMU responses of euro area countries to global risk aversion shocks have become similar to those of Italy, Portugal or Spain before EMU, i.e., of economies of the euro area’s periphery. Our findings also suggest that the divergence in external competitiveness among euro area countries over the last decade, which is at the core of today’s debate on the future of the euro area, is more likely due to country-specific shocks than to global shocks.

Hosotani Mechanism in Higher Dimensional Lee–Wick Theory

Hosotani mechanism in higher-dimensional Lee-Wick theory is investigated. The symmetry breaking mechanism proposed by Hosotani is studied at one-loop level through a toy model in this theory. We find that the phase diagram of symmetry and masses of fields are modified from the original one if masses of Lee-Wick particles are in the same order of the inverse of the compactification scale.

Extensions of the conformal representations for orthogonal Lie algebras

The conformal transformations with respect to the metric defining o(n,C) give rise to an inhomogeneous polynomial representation of o(n+2,C). Using Shenʼs technique of mixed product, we generalize the above representation to an inhomogeneous representation of o(n+2,C) on the tensor space of any finite-dimensional irreducible o(n,C)-module with the polynomial space, where a hidden central transformation is involved. Moreover, we find a condition on the constant value taken by the central transformation such that the generalized representation is irreducible. In our approach, Pieriʼs formulas, invariant operators and the idea of Kostantʼs characteristic identities play key roles. The result could be useful in understanding higher-dimensional conformal field theory with the constant value taken by the central transformation as the central charge. Our representations virtually provide natural extensions of the conformal transformations on a Riemannian manifold to its vector bundles.

On gravity localization under Lorentz violation in warped scenario

Recently Rizzo studied the Lorentz Invariance Violation (LIV) in a brane scenario with one extra dimension where he found a non-zero mass for the four-dimensional graviton. This leads to the conclusion that five-dimensional models with LIV are not phenomenologically viable. In this work we re-examine the issue of Lorentz Invariance Violation in the context of higher-dimensional theories. We show that a six-dimensional geometry describing a string-like defect with a bulk-dependent cosmological constant can yield a massless 4D graviton, if we allow the cosmological constant variation along the bulk, and thus can provides a phenomenologically viable solution for the gauge hierarchy problem.

An upper bound of essential norm of composition operator on H 2(B n )

The authors give an upper bound of the essential norm of a composition operator on H2(Bn), which involves the counting function in the higher dimensional value distribution theory defined by S. S. Chern. A criterion is also given to assure that the composition operator on H2(Bn) is bounded or compact.

Higher-dimensional cluster combinatorics and representation theory

Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite-dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied. Cyclic polytopes are classical objects of study in convex geometry. In particular, their triangulations have been studied with a view towards generalizing the rich combinatorial structure of triangulations of polygons. In this paper, we demonstrate a connection between these two seemingly unrelated subjects. We study triangulations of even-dimensional cyclic polytopes and tilting modules for higher Auslander algebras of linearly oriented type A which are summands of the cluster tilting module. We show that such tilting modules correspond bijectively to triangulations. Moreover mutations of tilting modules correspond to bistellar flips of triangulations. For any d -representation finite algebra we introduce a certain d -dimensional cluster category and study its cluster tilting objects. For higher Auslander algebras of linearly oriented type A we obtain a similar correspondence between cluster tilting objects and triangulations of a certain cyclic polytope. Finally we study certain functions on generalized laminations in cyclic polytopes, and show that they satisfy analogues of tropical cluster exchange relations. Moreover we observe that the terms of these exchange relations are closely related to the terms occurring in the mutation of cluster tilting objects.

Quantum degenerate systems

A degenerate dynamical system is characterized by a symplectic structure whose rank is not constant throughout phase space. Its phase space is divided into causally disconnected, nonoverlapping regions in each of which the rank of the symplectic matrix is constant, and there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems—in which the degeneracy cannot be eliminated by redefining variables in the action—the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.

New states of gauge theories on a circle

We study a one-dimensional large-N U(N) gauge theory on a circle as a toy model of higher dimensional Yang-Mills theories at finite temperature. To investigate the profile of the thermodynamical potential in this model, we evaluate a stochastic time evolution of several states, and find that an unstable confinement phase at high temperature does not decay to a stable deconfinement phase directly. Before it reaches the deconfinement phase, it develops to several intermediate states. These states are characterised by the expectation values of the Polyakov loop operators, which wind the temporal circle different times. We reveal that these intermediate states are the saddle point solutions of the theory, and similar solutions exist in a wide class of SU(N) and U(N) gauge theories on S 1 including QCD and pure Yang-Mills theories in various dimensions. We also consider a Kaluza-Klein gravity, which is the gravity dual of the one-dimensional gauge theory on a spatial S 1, and show that these solutions may be related to multi black holes localised on the S 1. Then we present a connection between the stochastic time evolution of the gauge theory and the dynamical decay process of a black string though the Gregory-Laflamme instability.

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G 2, Spin(7), O(8) as well as E 8 and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.

Superfield formalism for 5D Lorentz violating models

We construct a supersymmetric higher dimensional theory which includes 5D Lorentz violation terms in a superfield formalism. We show that in order to obtain a consistent construction which incorporates the most general terms that explicitly breaks the 5D Lorentz invariance, it is only necessary to redefine the supersymmetric auxiliary fields. We also analyze the meaning of these violation terms and point out the possibility of resizing the radius of compactification to obtain an equivalent 4D Lorentz invariant effective theory.

The Teodorescu operator in Clifford analysis

Euclidean Clifford analysis is a higher dimensional function theory centred around monogenic functions, i.e., null solutions to a first order vector valued rotation invariant differential operator \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\partial }\) called the Dirac operator. More recently, Hermitian Clifford analysis has emerged as a new branch, offering yet a refinement of the Euclidean case; it focuses on the simultaneous null solutions, called Hermitian monogenic functions, to two Hermitian Dirac operators \(\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} }\) and \(\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} ^\dag }\) which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Teodorescu operator is the right inverse of the Dirac operator \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\partial }\). In this paper, Teodorescu operators for the Hermitian Dirac operators \(\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} }\) and \(\partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} ^\dag }\) are constructed. Moreover, the structure of the Euclidean and Hermitian Teodorescu operators is revealed by analyzing the more subtle behaviour of their components. Finally, the obtained inversion relations are still refined for the differential operators issuing from the Euclidean and Hermitian Dirac operators by splitting the Clifford algebra product into its dot and wedge parts. Their relationship with several complex variables theory is discussed.

Noninteraction of Waves in Two-dimensional Conformal Field Theory

In higher dimensional quantum field theory, irreducible representations of the Poincare group are associated with particles. Their counterpart in two-dimensional massless models are "waves" introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Moebius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Moebius covariant net from the vacuum. It is also shown that Bisognano-Wichmann property, dilation covariance and asymptotic completeness (with respect to waves) imply Moebius symmetry. Under natural assumptions, we observe that the maps which give asymptotic fields in Poincare covariant theory are conditional expectations between appropriate algebras. We show that a two-dimensional massless theory is asymptotically complete and noninteracting if and only if it is a chiral Moebius covariant theory.