Monstrous Branes

 We study D-branes in the bosonic closed string theory whose automorphism group is the Bimonster group (the wreath product of the Monster simple group with ℤ₂). We give a complete classification of D-branes preserving the chiral subalgebra of Monster invariants and show that they transform in a representation of the Bimonster. Our results apply more generally to self-dual conformal field theories which admit the action of a compact Lie group on both the left- and right-moving sectors. Received: 20 February 2002 / Accepted: 17 August 2002 Published online: 19 December 2002 Communicated by R.H. Dijkgraaf     

Branes and wrapping rules

We show that the branes of ten-dimensional IIA/IIB string theory must satisfy, upon toroidal compactification, specific wrapping rules in order to reproduce the number of supersymmetric branes that follows from a supergravity analysis. The realization of these wrapping rules suggests that IIA/IIB string theory contains a whole class of generalized Kaluza-Klein monopoles.     

Branes and Calibrated Geometries

The fivebrane worldvolume theory in eleven dimensions is known to contain BPS threebrane solitons which can also be interpreted as a fivebrane whose worldvolume is wrapped around a Riemann surface. By considering configurations of intersecting fivebranes and hence intersecting threebrane solitons, we determine the Bogomol'nyi equations for more general BPS configurations. We obtain differential equations, generalising Cauchy–Riemann equations, which imply that the worldvolume of the fivebrane is wrapped around a calibrated submanifold. Received: 20 April 1998 / Accepted: 16 November 1998     

Quasi-gravity in Branes

In contrast with pseudo-gravitational effects that are mathematically analogous but physically quite distinct from gravity, this presentation deals with a kind of quasi-gravitational effect that can act in an asymmetrically moving brane worldsheet in a manner that approximates (and in a crude analysis might be physically indistinguishable from) the effect that would arise from genuine gravitation, of ordinary Newtonian type in nonrelativistic applications and of scalar–tensor (Jordan–Brans–Dicke rather than pure Einstein) type in relativistic applications.     

Shortcuts in Cosmological Branes

We aim at gathering information from gravitational interaction in the Universe, at energies where quantum gravity is required. In such a setup a dynamical membrane world in a space-time with scalar bulk matter described by domain walls, as well as a dynamical membrane world in empty Anti de Sitter space-time, is analyzed. We later investigate the possibility of having shortcuts for gravitons leaving the membrane and returning subsequently. In comparison with photons following a geodesic inside the brane, we verify that shortcuts exist. For late time universes they are small, but for some primordial universes they can be quite effective. In the case of matter branes, we argue that at times just before nucleosynthesis the effect is sufficiently large to provide corrections to the inflationary scenario, especially as concerning the horizon problem and the Cosmological Background Radiation.     

Dynamics of Strings and Branes

We study Nambu–Goto strings and branes. It is shown that they can be considered as continuous limits of ordered discrete sets of relativistic particles for which the tangential velocities are excluded from the action. The linear in unphysical momenta constraints are found. It allows to derive the evolution operators for the objects under consideration from the “first principles.”     

Branes wrapping black holes

We examine the dynamics of extended branes, carrying lower-dimensional brane charges, wrapping black holes and black hole microstates in M and type II string theory. We show that they have a universal dispersion relation typical of threshold bound states with a total energy equal to the sum of the contributions from the charges. In near-horizon geometries of black holes, these are BPS states, and the dispersion relation follows from supersymmetry as well as properties of the conformal algebra. However they break all supersymmetries of the full asymptotic geometries of black holes and microstates. We comment on a recent proposal which uses these states to explain black hole entropy.     

World-Volume Fields and Background Coupling of Branes

After giving a brief introduction to the conceptof branes and their role in string theory, this paperdescribes a method for formulating the dynamics ofbranes, especially those containing nonscalar moduli. Emphasis is put on the coupling of branes tofields in the low-energy background supergravitytheories, and on preservation of maximal amount ofmanifest symmetry. The presentation is aimed atphysicists who are not experts in string theory.     

Gradient Formula for Linearly Self-Interacting Branes

 The computation of long range linear self-interaction forces in string and higher dimensional brane models requires the evaluation of the gradients of regularised values of divergent self-interaction potentials. It is shown that the appropriately regularised gradient in directions orthogonal to the brane surface will always be obtainable simply by multiplying the regularised potential components by just half the trace of the second fundamental tensor, except in the hypermembrane case for which the method fails. Whatever the dimension of the background this result is valid provided the codimension is two (the hyperstring case) or more, so it can be used for investigating brane-world scenarios with more than one extra space dimension. Received: 15 April 2002 / Accepted: 23 October 2002 Published online: 25 February 2003 Communicated by H. Nicolai     

Magnetic Branes in Brans-Dicke-Maxwell Theory

We present a new class of magnetic brane solutions in (n+1)-dimensional Brans-Dicke-Maxwell theory in the presence of a quadratic potential for the scalar field. These solutions are neither asymptotically flat nor (anti)-de Sitter. Our strategy for constructing these solutions is applying a conformal transformation to the corresponding solutions in dilaton gravity. This class of solutions represents a spacetime with a longitudinal magnetic field generated by a static brane. They have no curvature singularity and no horizons but have a conic geometry with a deficit angle δ. We generalize this class of solutions to the case of spinning magnetic brane with all rotation parameters. We also use the counterterm method and calculate the conserved quantities of the solutions.     

String Scattering from Decaying Branes

We develop the general formalism of string scattering from decaying D-branes in bosonic string theory. In worldsheet perturbation theory, amplitudes can be written as a sum of correlators in a grand canonical ensemble of unitary random matrix models, with time setting the fugacity. An approach employed in the past for computing amplitudes in this theory involves an unjustified analytic continuation from special integer momenta. We give an alternative formulation which is well-defined for general momenta. We study the emission of closed strings from a decaying D-brane with initial conditions perturbed by the addition of an open string vertex operator. Using an integral formula due to Selberg, the relevant amplitude is expressed in closed form in terms of zeta functions. Perturbing the initial state can suppress or enhance the emission of high energy closed strings for extended branes, but enhances it for D0-branes. The closed string two point function is expressed as a sum of Toeplitz determinants of certain hypergeometric functions. A large N limit theorem due to Szegö, and its extension due to Borodin and Okounkov, permits us to compute approximate results showing that previous naive analytic continuations amount to the large N approximation of the full result. We also give a free fermion formulation of scattering from decaying D-branes and describe the relation to a grand canonical ensemble for a 2d Coulomb gas.     

Star Products and Branes in Poisson-Sigma Models

We prove that non-coisotropic branes in the Poisson-Sigma model are allowed at the quantum level. When the brane is defined by second-class constraints, the perturbative quantization of the model yields Kontsevich’s star product associated to the Dirac bracket on the brane. Finally, we present the quantization for a general brane.Research supported by grant FPU, MEC (Spain).Research supported by grant FPA2003-02948, MEC (Spain).     

Stability of Black Holes and Black Branes

We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, ${\mathcal{E}}$ , on a subspace, ${\mathcal{T}}$ , of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that—apart from pure gauge perturbations and perturbations towards other stationary black holes— ${\mathcal{E}}$ is nondegenerate on ${\mathcal{T}}$ and that, for axisymmetric perturbations, ${\mathcal{E}}$ has positive flux properties at both infinity and the horizon. We further show that ${\mathcal{E}}$ is related to the second order variations of mass, angular momentum, and horizon area by ${\mathcal{E} = \delta^2 M -\sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi}\delta^2 A}$ , thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with ${\mathcal{E} < 0}$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of ${\mathcal{E}}$ on ${\mathcal{T}}$ is equivalent to the satisfaction of a “ local Penrose inequality,” thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability. Although we restrict our considerations in this paper to vacuum general relativity, most of the results of this paper are derived using general Lagrangian and Hamiltonian methods and therefore can be straightforwardly generalized to allow for the presence of matter fields and/or to the case of an arbitrary diffeomorphism covariant gravitational action.     

Calibrations and T–Duality

For a subclass of Hitchin’s generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated submanifolds minimise a functional occurring as D–brane energy in type II string theories. Further, we investigate the behaviour of calibrated cycles under T–duality and construct non–trivial examples.     

Study of Branes with Variable Tension

In this work we study a brane world model with variable tension, which gives rise to four-dimensional cosmologies. The brane worlds obtained correspond to E?tv?s branes whose(internal) geometry can be casted as either a four-dimensional(A)dS_4 or a standard radiation period cosmology. The matter dominated period is discussed as well.