Extremal P-branes Research Articles

Fractional branes, warped compactifications and backreacted orientifold planes

Abstract The standard extremal p-brane solutions in supergravity are known to allow for a generalisation which consists of adding a linear dependence on the worldvolume coordinates to the usual harmonic function. In this note we demonstrate that remarkably this generalisation goes through in exactly the same way for p-branes with fluxes added to it that correspond to fractional p-branes. We relate this to warped orientifold compactifications by trading the Dp-branes for Op-planes that solve the RR tadpole condition. This allows us to interpret the worldvolume dependence as due to lower-dimensional scalars that flow along the massless directions in the no-scale potential. Depending on the details of the fluxes these flows can be supersymmetric domain wall flows. Our solutions provide explicit examples of backreacted orientifold planes in compactifications with non-constant moduli.

Pseudo-Killing spinors, pseudo-supersymmetric p-branes, bubbling and less-bubbling AdS spaces

We consider Einstein gravity coupled to an n-form field strength in D dimensions. Such a theory cannot be supersymmetrized in general, we nevertheless propose a pseudo-Killing spinor equation and show that the AdS X Sphere vacua have the maximum number of pseudo-Killing spinors, and hence are fully pseudo-supersymmetric. We show that extremal p-branes and their intersecting configurations preserve fractions of the pseudo-supersymmetry. We study the integrability condition for general (D,n) and obtain the additional constraints that are required so that the existence of the pseudo-Killing spinors implies the Einstein equations of motion. We obtain new pseudo-supersymmetric bubbling AdS_5 X S^5 spaces that are supported by a non-self-dual 5-form. This demonstrates that non-supersymmegtric conformal field theories may also have bubbling states of arbitrary droplets of free fermions in the phase space. We also obtain an example of less-bubbling AdS geometry in D=8, whose bubbling effects are severely restricted by the additional constraint arising from the integrability condition.

High-energy string-brane scattering: leading eikonal and beyond

We extend previous techniques for calculations of transplanckian-energy string-string collisions to the high-energy scattering of massless closed strings from a stack of N Dp-branes in Minkowski spacetime. We show that an effective non-trivial metric emerges from the string scattering amplitudes by comparing them against the semiclassical dynamics of high-energy strings in the extremal p-brane background. By changing the energy, impact parameter and effective open string coupling, we are able to explore various interesting regimes and to reproduce classical expectations, including tidal-force excitations, even beyond the leading-eikonal approximation.

FROM p-BRANES TO COSMOLOGY

We study the relationship between static p-brane solitons and cosmological solutions of string theory or M theory. We discuss two different ways in which extremal p-branes can be generalized to nonextremal ones, and show how wide classes of recently discussed cosmological models can be mapped into nonextremal p-brane solutions of one of these two kinds. We also extend previous discussions of cosmological solutions to include some that make use of cosmological-type terms in the effective action that can arise from the generalized dimensional reduction of string theory or M theory.

Massive-scalar absorption by extremal p-branes

We study the absorption probability of minimally-coupled massive scalars by extremal p-branes. In particular, we find that the massive scalar wave equation under the self-dual string background has the same form as the massless scalar wave equation under the dyonic string background. Thus it can be cast into the form of a modified Mathieu equation and solved exactly. Another example that we can solve exactly is that of the D=4 two-charge black hole with equal charges, for which we obtain the closed-form absorption probability. We also obtain the leading-order absorption probabilities for D3-, M2- and M5-branes.

Closed-form absorption probability of certain D = 5 and D = 4 black holes and leading-order cross-section of generic extremal p-branes

We obtain the closed-form absorption probabilities for minimally-coupled massless scalars propagating in the background of D=5 single-charge and D=4 two-charge black holes. These are the only two examples of extremal black holes with non-vanishing absorption probabilities that can be solved in closed form for arbitrary incident frequencies. In both cases, the absorption probability vanishes when the frequency is below a certain threshold, and we discuss the connection between this phenomenon and the behaviour of geodesics in these black hole backgrounds. We also obtain leading-order absorption cross-sections for generic extremal p-branes, and show that the expression for the cross-section as a function of frequency coincides with the leading-order dependence of the entropy on the temperature in the corresponding near-extremal p-branes.

INTERACTING INTERSECTIONS

Intersecting p-branes can be viewed as higher-dimensional interpretations of multicharge extremal p-branes, where some of the individual p-branes undergo diagonal dimensional oxidation, while the others oxidize vertically. Although the naive vertical oxidation of a single p-brane gives a continuum of p-branes, a more natural description arises if one considers a periodic array of p-branes in the higher dimension, implying a dependence on the compactification coordinates. This still reduces to the single lower-dimensional p-brane when viewed at distances large compared with the period. Applying the same logic to the multicharge solutions, we are led to consider more general classes of intersecting p-brane solutions, again depending on the compactification coordinates, which turn out to be described by interacting functions rather than independent harmonic functions. These new solutions also provide a more satisfactory interpretation for the lower-dimensional multicharge p-branes, which otherwise appear to be nothing more than the improbable coincidence of charge-centres of individual constituents with zero binding energy.

Rules for localized overlappings and intersections of p-branes

We determine an intersection rule for extremal p-branes which are localized in their relative transverse coordinates by solving, in a purely bosonic context, the equations of motion of gravity coupled to a dilaton and n-form field strengths. The unique algebraic rule we obtained does not lead to new solutions while it manages to collect, in a systematic way, most of the solutions (all those compatible with our ansatz) that have appeared in the literature. We then consider bound states of zero binding energy where a third brane is accomodated in the common and overall transverse directions. They are given in terms of non-harmonic functions. A different algebraic rule emerges for these last intersections, being identical to the intersection rule for p-branes which only depend on the overall transverse coordinates. We clarify the origin of this coincidence. The whole set of solutions in ten and eleven dimensional theories is connected by dualities and dimensional reductions. They are related to brane configurations recently used to study non-perturbative phenomena in supersymmetric gauge theories.

HARMONIC SUPERPOSITIONS OF NONEXTREMAL p-BRANES

The plot of allowed p and D values for p-brane solitons in D-dimensional supergravity is the same whether the solitons are extremal or nonextremal. One of the useful tools for relating different points on the plot is vertical dimensional reduction, which is possible if periodic arrays of p-brane solitons can be constructed. This is straightforward for extremal p-branes, since the no-force condition allows arbitrary multicenter solutions to be constructed in terms of a general harmonic function on the transverse space. This has also been shown to be possible in the special case of nonextremal black holes in D=4 arrayed along an axis. In this paper, we extend previous results to include multiscalar black holes, and dyonic black holes. We also consider their oxidation to higher dimensions, discuss general procedures for constructing the solutions and study their symmetries.

Non-extremal intersecting p-branes in various dimensions

Non-extremal intersecting p-brane solutions of gravity coupled with several antisymmetric fields and dilatons in various space-time dimensions are constructed. The construction uses the same algebraic method of finding solutions as in the extremal case and a modified "no-force" conditions. We justify the "deformation" prescription. It is shown that the non-extremal intersecting p-brane solutions satisfy harmonic superposition rule and the intersections of non-extremal p-branes are specified by the same characteristic equations for the incidence matrices as for the extremal p-branes. We show that S-duality holds for non-extremal p-brane solutions. Generalized T-duality takes place under additional restrictions to the parameters of the theory which are the same as in the extremal case.

Gravitational lensing by p-branes

The scattering of R-R gauge bosons off of Dirichlet p-branes is computed to leading order in the string coupling. The results are qualitatively similar to those found in the scattering of massless NS-NS bosons: all p-branes with p ≥ 0 exhibit stringy properties, in particular the Regge behavior. Both the R-R and NS-NS scattering amplitudes agree in the limit of small momentum transfer with scattering off the extremal R-R charged p-brane solutions found in the low-energy supergravities. We interpret this as evidence that Dirichlet-branes are an exact worldsheet description of the extremal p-branes. The −1-brane (D-instanton) is a special object which, unlike all other Dirichlet-branes, exhibits point-like behavior. We show that the field theoretic scattering off of the R-R charged instanton solution to type IIB supergravity exactly reproduces the full stringy calculation. As an aside, we include a discussion of the entropy of nonextremal black holes in ten dimensions, produced by exciting the 0-brane.

Rusty scatter branes

We derive double-dimensional reduction/oxidation in a framework where it is applicable to describe general nonstatic (and anisotropic) p-brane solutions. Given this procedure, we are able to relate the dynamical interaction potential for parallel extremal p-branes in D dimensions to that for extremal black holes in D - p dimensions. In particular, we find that to leading order the potential vanishes for all K-symmetric p-branes.