Intersection Rules for S-Branes

We give a model-independent derivation of general intersecting rules for spacelike branes (S-branes) in arbitrary dimensions d. This is achieved by directly solving bosonic field equations for supergravity coupled to a dilaton and antisymmetric tensor fields with minimal ansätze. We compare the results with those in eleven-dimensional supergravity and other solutions. ∗e-mail address: [email protected] There has been much interest in time-dependent and spacelike brane solutions (Sbranes) of supergravities in eleven and ten dimensions because of its possible connection with tachyon condensations and dS/CFT correspondence [1, 2]. These theories are the low-energy limits of the string theories and supposedly unifying M-theory of strings. Timedependent solutions are investigated rather recently and not much is known on these solutions. It is thus important to better understand these classical p-brane solutions. The single p-brane solutions (Sp-branes) have been discussed in refs. [1, 3, 4, 5] for low-energy effective supergravities (see also refs. [6, 7] for related solutions). Following the usual convention, Sp-branes are used for those with (p + 1)-dimensional Euclidean world-volume. It has then been noted that the more general solutions can be understood as intersecting ones of these fundamental p-branes [8, 9] and the rules how the branes intersect with each other are given in analogy to the usual branes [10]–[14]. Although the “rules” are consistent with most of the known solutions, it is not clear if there are any other solutions than those given by these rules. The questions we would like to ask here are how general these rules are and how severely they restrict the solutions for supergravities in d = 11 and lower dimensions. A systematic approach to formulating the rules for the way how they can intersect has been derived for the usual branes in [13, 14]. The purpose of this note is to extend this work to the S-branes and clarify what ansätze are really necessary. In particular, we derive the intersection rules from the general approach. We show that the rules are simple consequences of the field equations, which can be easily integrated and the consistency of the solutions reduces the problem of solving the field equations to an algebraic one. The results of our analysis turn out to be consistent with the superposition rules in ref. [8] for d = 11 supergravity, but our results apply to more general supergravity coupled to a dilaton and antisymmetric tensors. We show that the requirement that the fields for the each brane be independent is sufficient to give the solutions and intersection rules. Let us start with the general action for gravity coupled to a dilaton φ and m different nA-form field strengths: I = 1 16πGd ∫