ar X iv : h ep - t h / 98 03 00 6 v 2 1 4 M ay 1 99 9 HYPERBOLIC KAC - MOODY ALGEBRA FROM INTERSECTING P - BRANES
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چکیده
A subclass of recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes (one electric and two magnetic) contains a cosmological solution to D = 11 supergravity related to hyperbolic Kac-Moody algebra F 3 (of rank 3). This solution describes the non-Kasner power-law inflation. Here we consider recently discovered class of solutions with intersecting p-branes [1]. These solutions are governed by a set of harmonic functions. The number of harmonic functions in general is less then the number of p-branes (as it takes place in orthogonal case [2]-[16]). The solutions correspond to a block-orthogonal set of p-brane vectors U s (see (2.17) below) and may be considered as a Majumdar-Papapetrou type extension of for the extremal limit of " block-orthogonal " black holes recently found in [17] (for " orthogonal " black holes see [18, 19, 20, 21, 22, 23] and references therein.) For 1-block case the solution is governed by one harmonic function and for a special configuration may be related to some simple finite dimensional Lie algebra or infinite dimensional hyperbolic Kac-Moody (KM) algebra [24, 25]. The affine KM algebras do not appear among the solutions from [1]. Let us consider the simplest example of D = 11 supergravity [26] (corresponding to M-theory [27]). It is known [3, 4, 5] that the orthogonal (or A 1 + A 1) intersection rules for the M-theory read
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ar X iv : h ep - t h / 98 03 00 6 v 1 2 M ar 1 99 8 HYPERBOLIC KAC - MOODY ALGEBRA FROM INTERSECTING P - BRANES
A subclass of recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes (one electric and two magnetic) contains a cosmological solution to D = 11 supergravity related to hyperbolic Kac-Moody algebra F 3 (of rank 3). This soluti...
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تاریخ انتشار 1999