Black and super p-branes in diverse dimensions

M. J. Duff; J. X. Lu

doi:10.1016/0550-3213(94)90586-X

paper

Black and super p-branes in diverse dimensions

arXiv:hep-th/9306052 · doi:10.1016/0550-3213(94)90586-X

Abstract

We present a generic Lagrangian, in arbitrary spacetime dimension $D$ , describing the interaction of a dilaton, a graviton and an antisymmetric tensor of arbitrary rank $d$ . For each $D$ ~and~ $d$ , we find ``solitonic'' black $p ~$ -brane solutions where $p ~ = d ~ - 1$ ~and~ $d ~ = D - d - 2$ . These solutions display a spacetime singularity surrounded by an event horizon, and are characterized by a mass per unit $p ~$ -volume, $M_{d ~}$ , and topological ``magnetic'' charge $g_{d ~}$ , obeying $κ M_{d ~} \geq g_{d ~} / 2$ . In the extreme limit $κ M_{d ~} = g_{d ~} / 2$ , the singularity and event horizon coalesce. For specific values of $D$ ~and~ $d$ , these extreme solutions also exhibit supersymmetry and may be identified with previously classified heterotic, Type IIA and Type IIB super $p ~$ -branes. The theory also admits elementary $p$ -brane solutions with ``electric'' Noether charge $e_{d}$ , obeying the Dirac quantization rule $e_{d} g_{d ~} = 2 π n$ , $n =$ ~integer. We also present the Lagrangian describing the theory dual to the original theory, whose antisymmetric tensor has rank $d ~$ and for which the roles of topological and elementary solutions are interchanged. The super $p$ -branes and their duals are mutually non-singular. As special cases of our general solution we recover the black $p$ -branes of Horowitz and Strominger $(D = 10)$ , Guven $(D = 11)$ and Gibbons et al $(D = 4)$ , the $N = 1$ , $N = 2 a$ ~and~ $N = 2 b$ super- $p$ -branes of Dabholkar et al $(4 \leq D \leq 10)$ , Duff and Stelle $(D = 11)$ , Duff and Lu $(D = 10)$ and Callan, Harvey and Strominger $(D = 10)$ , and the axionic instanton of Rey $(D = 4)$ . In particular, the electric/magnetic duality of Gibbons and Perry in $D = 4$ is seen to be a consequence of particle/sixbrane duality in $D = 10$ . Among the new solutions is a self-dual superstring in $D = 6$ .

42 pages, harvmac, CERN-TH.6675/93, CTP/TAMU-54/92

Black and super p-branes in diverse dimensions

Abstract

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