4 research outputs found
Waves, boosted branes and BPS states in M-theory
Certain type II string non-threshold BPS bound states are shown to be related
to non-static backgrounds in 11-dimensional theory. The 11-d counterpart of the
bound state of NS-NS and R-R type IIB strings wound around a circle is a pure
gravitational wave propagating along a generic cycle of 2-torus. The extremal
(q_1,q_2) string with non-vanishing momentum along the circle (or infinitely
boosted black string) corresponds in D=11 to a 2-brane wrapped around 2-torus
with momentum flow along the (q_1,q_2) cycle. Applying duality transformations
to the string-string solution we find type IIA background representing a bound
state of 2-brane and 0-brane. Its lift to 11 dimensions is simply a 2-brane
finitely boosted in transverse direction. This 11-d solution interpolates
between a static 2-brane (zero boost) and a gravitational wave in 11-th
dimension (infinite boost). Similar interpretations are given for various bound
states involving 5-branes. Relations between transversely boosted M-branes and
1/2 supersymmetric non-threshold bound states 2+0 and 5+0 complement relations
between M-branes with momentum in longitudinal direction and 1/4 supersymmetric
threshold bound states 1+0 and 4+0. In the second part of the paper we
establish the correspondence between the BPS states of type IIB strings on a
circle and oscillating states of a fundamental supermembrane wrapped around a
2-torus. We show that the (q_1,q_2) string spectrum is reproduced by the
membrane BPS spectrum, determined using a certain limit. This supports the
picture suggested by Schwarz.Comment: 26 pages, harvmac (minor corrections; T-duality relation between IIB
string-string solution and boosted 0-brane made explicit
Solutions with intersecting p-branes related to Toda chains
Solutions in multidimensional gravity with m p-branes related to Toda-like
systems (of general type) are obtained. These solutions are defined on a
product of n+1 Ricci-flat spaces M_0 x M_1 x...x M_n and are governed by one
harmonic function on M_0. The solutions are defined up to the solutions of
Laplace and Toda-type equations and correspond to null-geodesics of the
(sigma-model) target-space metric. Special solutions relating to A_m Toda
chains (e.g. with m =1,2) are considered.Comment: 20 pages, Latex, to be submit. to JM
Sigma-model for Generalized Composite p-branes
A multidimensional gravitational model containing several dilatonic scalar
fields and antisymmetric forms is considered. The manifold is chosen in the
form M = M_0 x M_1 x ... x M_n, where M_i are Einstein spaces (i > 0). The
block-diagonal metric is chosen and all fields and scale factors of the metric
are functions on M_0. For the forms composite (electro-magnetic) p-brane ansatz
is adopted. The model is reduced to gravitating self-interacting sigma-model
with certain constraints. In pure electric and magnetic cases the number of
these constraints is m(m - 1)/2 where m is number of 1-dimensional manifolds
among M_i. In the "electro-magnetic" case for dim M_0 = 1, 3 additional m
constraints appear. A family of "Majumdar-Papapetrou type" solutions governed
by a set of harmonic functions is obtained, when all factor-spaces M_k are
Ricci-flat. These solutions are generalized to the case of non-Ricci-flat M_0
when also some additional "internal" Einstein spaces of non-zero curvature are
added to M. As an example exact solutions for D = 11 supergravity and related
12-dimensional theory are presented.Comment: 33 pages, Latex. Some corrections and rearrangements are mad