Brane Potentials and Moduli Spaces

It is shown that the supergravity moduli spaces of D1-D5 and D2-D6 brane systems coincide with those of the Coulomb branches of the associated non-abelian gauge theories. We further discuss situations in which worldvolume brane actions include a potential term generated by probing certain supergravity backgrounds. We find that in many cases, the appearance of the potential is due to the application of the Scherk-Schwarz mechanism. We give some examples and discuss the existence of novel supersymmetric brane configurations.Comment: 26 pages, phyzzx.te

Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities

We classify (up to local isometry) the maximally supersymmetric solutions of the eleven- and ten-dimensional supergravity theories. We find that the AdS solutions, the Hpp-waves and the flat space solutions exhaust them.Comment: 24 page

Pluecker-type relations for orthogonal planes

We explore a Pluecker-type relation which occurs naturally in the study of maximally supersymmetric solutions of certain supergravity theories. This relation generalises at the same time the classical Pluecker relation and the Jacobi identity for a metric Lie algebra and coincides with the Jacobi identity of a metric n-Lie algebra. In low dimension we present evidence for a geometric characterisation of the relation in terms of middle-dimensional orthogonal planes in euclidean or lorentzian inner product spaces.Comment: 39 pages (v2: substantial revision, 33% more material, link with n-Lie algebras

Non-BPS Dirac-Born-Infeld Solitons

We show that CPn sigma model solitons solve the field equations of a Dirac-Born-Infeld (DBI) action and, furthermore, we prove that the non-BPS soliton/anti-soliton solutions of the sigma model also solve the DBI equations. Using the moduli space approximation we compare the dynamics of the BPS sigma model solitons with that of the associated DBI solitons. We find that for the CP1 case the metric on the moduli space of sigma model solitons is identical to that of the moduli space of DBI solitons, but for CPn with n>1 we show that the two metrics are not equal. We also consider the possibility of similar non-BPS solitons in other DBI theories.Comment: Major changes; sections removed and title changed. Version published in JHE

Covariantly constant forms on torsionful geometries from world-sheet and spacetime perspectives

The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a Nijenhuis form, and that there may be further reductions of the structure group. In many cases of interest there are also covariantly constant one-forms which also give rise to symmetries. These geometries are of interest in the context of heterotic supergravity solutions and the associated reductions are studied from a spacetime point of view via the Killing spinor equations.Comment: 33 pages, minor modifications, version published in JHE

Semi-global symplectic invariants of the Euler top

The semi-global symplectic invariants were introduced by Dufour et. al. as a means of verifying equivalence of integrable systems in one degree of freedom. In the main part of the thesis we explicitly compute the semi-global symplectic invariants near the hyperbolic equilibrium point of the Euler top, otherwise known as the rigid body. As an interim step, the Birkhoff normal form of the Hamiltonian at this point is computed using Lie series. The Picard-Fuchs ODE for the action near the hyperbolic equilibrium is derived. Using the method of Frobenius on the Picard-Fuchs equation we show that the Birkhoff normal form can also be found by inverting the Frobenius series of the regular action integral. Composition of the regular action integral with the singular action integral leads to the symplectic invariant. To our knowledge this is the first time that such invariants near a hyperbolic point have been computed explicitly using the Picard-Fuchs equation. Finally we discuss the convergence of these invariants using both analytical and numerical arguments, as well as explore the possibility of equivalence with the pendulum

The Universality of Penrose Limits near Space-Time Singularities

We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u^{-2}-behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic power-law singularities of this type the oscillator frequencies of the resulting homogeneous singular plane wave turn out to lie in a range which is known to allow for an analytic extension of string modes through the singularity. The discussion is phrased in terms of the recently obtained covariant characterisation of the Penrose limit; the relation with null geodesic deviation is explained in detail.Comment: 36 pages, LaTeX2e, 4 figure

Penrose limits and maximal supersymmetry

We show that the maximally supersymmetric pp-waves of IIB superstring and M-theories can be obtained as a Penrose limit of the supersymmetric AdS x S solutions. In addition we find that in a certain large tension limit, the geometry seen by a brane probe in an AdS x S background is either Minkowski space or a maximally supersymmetric pp-wave.Comment: 12 pages, v2: references adde