Rules for localized overlappings and intersections of p-branes

Abstract

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.

On the stability of (M theory) stars against collapse: Role of anisotropic pressures

“…The equations of state in [45,46,55,59,60,61,56,57], which were obtained by other methods, all obey these U duality relations.…”

“…Assuming the spatial directions of the brane worldvolumes to be toroidal and assuming necessary isometries, the M theory brane configurations consisting of N stacks of two and five branes which intersect according to BPS rules, can be described by N seperately conserved energy momentum tensors T M N (I) , I = 1, 2, · · · , N , with appropriate equations of state among their components. See [59,60,61] and the references therein. The equations of state may follow from an action; or they may be derived using the microscopic dynamics of the constituents which are far from being rigorously known; or they may simply be postulated as an ansatz.…”

“…The M theory stars are eleven dimensional and are assumed to be made up of N stacks of M2 and M5 branes, intersecting according to the BPS rules whereby two stacks of five branes intersect along three common spatial directions; a stack each of two branes and five branes intersect along one common spatial direction; and two stacks of two branes intersect along zero common spatial direction. Assuming the spatial directions of the brane worldvolumes to be toroidal and assuming necessary isometries, the intersecting M theory branes can be described by N seperately conserved energy momentum tensors T M N (I) , I = 1, 2, · · · , N , with appropriate equations of state among their components [55,59,60,61,56,57,58,63,64,65].…”

“…We take the spatial directions of the brane worldvolumes to be toroidal and assume necessary isometries. These intersecting branes can be modelled by N number of seperately conserved energy momentum tensors [55,59,60,61]. Hence, the present formalism can be applied to the corresponding stars.…”

“…In M theory, equations describing black hole spacetimes follow from an eleven dimensional low energy effective action [45,46,55,59,60,61]. In the context of an expanding universe, the equations of state for intersecting branes have been derived in certain approximations using microscopic dynamics of branes [56,57].…”