Kaluza-Klein Monopole Research Articles

Nonlinear Perturbations of the Kaluza-Klein Monopole

We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five-dimensional vacuum Einstein equations. Using both numerical and analytical methods, we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi type-IX ansatz recently introduced by Bizoń, Chmaj, and Schmidt. We also show that for sufficiently large perturbations the Kaluza-Klein monopole loses stability and collapses to a Kaluza-Klein black hole. The relevance of our results for the stability of Bogomol'nyi-Prasad-Sommerfield states in M or string theory is briefly discussed.

DYNAMICAL (SUPER)SYMMETRIES OF MONOPOLES AND VORTICES

The dynamical (super)symmetries for various monopole systems are reviewed. For a Dirac monopole, non-smooth Runge–Lenz vector can exist; there is, however, a spectrum-generating conformal o(2,1) dynamical symmetry that extends into osp(1/1) or osp(1/2) for spin 1/2 particles. Self-dual 't Hooft–Polyakov-type monopoles admit an su(2/2) dynamical supersymmetry algebra, which allows us to reduce the fluctuation equation to the spin 0 case. For large r, the system reduces to a Dirac monopole plus a suitable inverse-square potential considered before by McIntosh and Cisneros, and by Zwanziger in the spin 0 case, and to the "dyon" of D'Hoker and Vinet for spin 1/2. The asymptotic system admits a Kepler-type dynamical symmetry as well as a "helicity-supersymmetry" analogous to the one Biedenharn found in the relativistic Kepler problem. Similar results hold for the Kaluza–Klein monopole of Gross–Perry–Sorkin. For the magnetic vortex, the N = 2 supersymmetry of the Pauli Hamiltonian in a static magnetic field in the plane combines with the o(2) × o(2,1) bosonic symmetry into an o(2) × osp(1/2) dynamical superalgebra.

On the gravitational energy of the Kaluza–Klein monopole

We use local counterterm prescriptions for asymptotically flat space to compute the action and conserved quantities in five-dimensional Kaluza–Klein theories. As an application of these prescriptions we compute the mass of the Kaluza–Klein magnetic monopole. We find consistent results with previous approaches that employ a background subtraction.

BIANCHI IX GROUP-MANIFOLD REDUCTIONS OF GRAVITY

We exhibit a new way to perform the group-manifold reduction of pure Einstein gravity in the vielbein formulation when the compactification group manifold is S3. The new Bianchi IX group-manifold reduction is obtained by exploiting the two three-dimensional Lie algebras that the S3 group manifold admits. As an application of the new reduction we show that there exists a domain wall solution to the lower-dimensional theory which upon uplifting to the higher-dimension turns out to be the self-dual (in the nonvanishing components of both curvature and spin connection) Kaluza–Klein monopole.

Worldsheet instanton corrections to the Kaluza-Klein monopole

The Kaluza-Klein monopole is a well known object in both gravity and string theory, related by T-duality to a ``smeared'' NS5-brane which retains the isometry around the duality circle. As the true NS5-brane solution is localized at a point on the circle, duality implies that the Kaluza-Klein monopole should show some corresponding behavior. In this paper, we express the Kaluza-Klein monopole as a gauged linear sigma model in two dimensions and show that worldsheet instantons give corrections to its geometry. These corrections can be understood as a localization in ``winding space'' which could be probed by strings with winding charge around the circle.

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.

Gravitational dielectric effect and Myers effect

In this paper we study the gravitational dielectric phenomena of a D2-brane in the background of Kaluza-Klein monopoles and D6-branes. In both cases the spherical D2-brane with nonzero radius becomes classical solution of the D2-brane action. We also investigate the gravitational Myers effect in the background of D6-branes. This phenomenon occurs since the tension of the D2-brane balances with the repulsive force between D0-branes and D6-branes.

S3 Group-manifold reduction of gravity

In this contribution we exhibit a new consistent group-manifold reduction of pure Einstein gravity in the vielbein formulation when the compactification group manifold is S3. The novel feature in the reduction is to consider the two 3-dimensional Lie algebras that S3 admits. We discuss the characteristics of the lower-dimensional theory and we emphasize the results generated by the new group-manifold reduction. As an application we show that the lower-dimensional theory admits a domain wall solution which upon uplifting to the higherdimension results to be the self-dual (in both curvature and spin connection) Kaluza-Klein monopole.

Wrapped D-branes as BPS monopoles: The moduli space perspective

We study the four dimensional effective action of a system of D6-branes wrapped on the $K3$ manifold times a torus, allowing the volume of the internal manifolds to remain dynamical. An unwrapped brane is at best a Dirac monopole of the dual RR sector field to which it couples. After wrapping, a brane is expected to behave as a BPS monopole, where the Higgs vacuum expectation value is set by the size of the $K3.$ We determine the moduli space of an arbitrary number of these wrapped branes by introducing a time dependent perturbation of the static solution and expanding the supergravity equations of motion to determine the dynamics of this perturbation, in the low velocity limit. The result is the hyper-K\"ahler generalization of the Euclidean Taub-NUT metric presented by Gibbons and Manton. We note that our results also pertain to the behavior of bound states of Kaluza-Klein monopoles and wrapped NS5-branes in the ${T}^{4}$ compactified heterotic string.

Gauged supergravities from Bianchi's group manifolds

We construct maximal D = 8 gauged supergravities by the reduction of D = 11 supergravity over three-dimensional group manifolds. Such manifolds are classified into two classes, A and B, and eleven types. This Bianchi classification carries over to the gauged supergravities. The class A theories have 1/2 BPS domain wall solutions that uplift to purely gravitational solutions consisting of 7D Minkowski and a 4D Euclidean geometry. These geometries are generically singular. The two regular exceptions correspond to the near-horizon limit of the single- or double-centre Kaluza–Klein monopole. In contrast, the class B supergravities are defined by a set of equations of motion that cannot be integrated to an action and allow for no 1/2 BPS domain walls.

G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions

We present a tentative formulation of theories of gravity with suitable matter content, including in particular pure gravity in D dimensions, the bosonic effective actions of M-theory and of the bosonic string, in terms of actions invariant under very-extended Kac-Moody algebras G+++. We conjecture that they host additional degrees of freedom not contained in the conventional theories. The actions are constructed in a recursive way from a level expansion for all very-extended algebras G+++. They constitute non-linear realisations on cosets, a priori unrelated to space-time, obtained from a modified Chevalley involution. Exact solutions are found for all G+++. They describe the algebraic properties of BPS extremal branes, Kaluza-Klein waves and Kaluza-Klein monopoles. They illustrate the generalisation to all G+++ invariant theories of the well-known duality properties of string theories by expressing duality as Weyl invariance in G+++. Space-time is expected to be generated dynamically. In the level decomposition of E8+++ = E11, one may indeed select an A10 representation of generators Pa which appears to engender space-time translations by inducing infinite towers of fields interpretable as field derivatives in space and time.

Kaluza-Klein monopole in AdS spacetime

We construct analogs of the flat space Kaluza-Klein (KK) monopoles in locally Anti-de Sitter (AdS) spaces for $D \ge 5+1$. We show that, unlike the flat space KK monopole, there is no five dimensional static KK monopole in AdS that smoothly reduces to the flat space one as the cosmological constant goes to zero. Thus, one needs at least two extra dimensions, one of which is compact, to get a static KK monopole in cosmological backgrounds.

Deconstructing KK monopoles

We describe a procedure for finding Kaluza-Klein monopole solutions in deconstructed four and five dimensional supersymmetric gauge theories. In the deconstruction of a four dimensional theory, the KK monopoles are finite-action solutions of the Euclidean equations of motion of the finite lattice spacing theory. The "lattice" KK monopoles can be viewed as constituents of continuum-limit four dimensional instantons. In the five dimensional case, the KK monopoles are static finite-energy stringlike configurations, wrapped and twisted around the compact direction, and can similarly be interpreted as constituents of five dimensional finite-energy gauge solitons. We discuss the quantum numbers and zero modes of the towers of deconstructed KK monopoles and their significance for understanding anomalies and nonperturbative effects in deconstruction.

Supersymmetric Kaluza–Klein reductions of M-waves and MKK-monopoles

We investigate the Kaluza–Klein reductions to ten dimensions of the purely gravitational half-BPS M-theory backgrounds: the M-wave and the Kaluza–Klein monopole. We determine the moduli space of smooth (supersymmetric) Kaluza–Klein reductions by classifying the freely acting spacelike Killing vectors which preserve some Killing spinor. As a consequence we find a wealth of new supersymmetric IIA configurations involving composite and/or bound-state configurations of waves, D0 and D6-branes, Kaluza–Klein monopoles in type IIA and flux/nullbranes, and some other new configurations. Some new features raised by the geometry of the Taub–NUT space are discussed, namely the existence of reductions with no continuous moduli. We also propose an interpretation of the flux 5-brane in terms of the local description (close to the branes) of a bound state of D6-branes and ten-dimensional Kaluza–Klein monopoles.

Macroscopic open strings and gravitational confinement

We consider classical solutions for strings ending on magnetically charged black holes in four-dimensional Kaluza–Klein theory. We examine the classical superstring and the global vortex, which can be viewed as a nonsingular model for the superstring. We show how both of these can end on a Kaluza–Klein monopole in the absence of self-gravity. Including gravitational back-reaction gives rise to a confinement mechanism of the magnetic flux of the black hole along the direction of the string. We discuss the relation of this work to localized solutions in ten-dimensional supergravity.

Hierarchy of Dirac, Pauli, and Klein–Gordon conserved operators in Taub-NUT background

The algebra of conserved observables of the SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza–Klein monopole is investigated. It is shown that the Dirac conserved operators have physical parts associated with Pauli operators that are also conserved in the sense of the Klein–Gordon theory. In this way one gets simpler methods of analyzing the properties of the conserved Dirac operators and their main algebraic structures including the representations of dynamical algebras governing the Dirac quantum modes.

The polarization of M5 branes and little string theories with reduced supersymmetry

We construct an M-theory dual of a 6-dimensional self-dual string theory with reduced supersymmetry, along the lines of Polchinski and Strassler. We find that upon perturbing the (2,0) theory with an R-current, the M5-branes polarize into a wrapped Kaluza Klein monopole, whose isometry direction is along the R current. We investigate the properties of this theory.

Noncommutative branes from M theory

The analysis of the worldvolume effective actions of the M-theory Kaluza-Klein monopole and 9-brane suggests that it should be possible to describe non-abelian configurations of M2-branes or M5-branes if the M2-branes are transverse to the eleventh direction and the M5-branes are wrapped on it. This is determined by the fact that the Kaluza-Klein monopole and the M9-brane are constrained to move in particular isometric spacetimes. We show that the same kind of situation is implied by the analysis of the brane descent relations in M-theory. We compute some of the non-commutative couplings of the worldvolume effective actions of these non-abelian systems of M2 and M5 branes and show that they indicate the existence of configurations corresponding to N branes expanding into a higher dimensional M-brane. The reduction to Type II brings up new descriptions of coincident D-branes at strong coupling. We show that these systems have the right non-commutative charges to describe certain expanded configurations playing a role in the framework of the AdS/CFT correspondence. Finally, we discuss the realization of non-commutative brane configurations as topological solitons in non-abelian brane-antibrane systems.

Duality in gravity and higher spin gauge fields

Dual field theory realisations are given for linearised gravity in terms of gauge fields in exotic representations of the Lorentz group. The field equations and dual representations are discussed for a wide class of higher spin gauge fields. For non-linear Einstein gravity, such transformations can be implemented locally in light-cone gauge, or partially implemented in the presence of a Killing vector. Sources and the relation to Kaluza-Klein monopoles are discussed.

Dynamical algebra and Dirac quantum modes in the Taub-NUTbackground

The SO(4,1) gauge-invariant theory of the Dirac fermions in theexternal field of the Kaluza-Klein monopole is investigated. It is shownthat the discrete quantum modes are governed by reduciblerepresentations of the o(4) dynamical algebra generated by thecomponents of the angular momentum operator and those of theRunge-Lenz operator of the Dirac theory in the Taub-NUT background. Theconsequence is that there exist central and axial discrete modes whosespinors have no separated variables.