Penrose limits, supergravity and brane dynamics

Abstract

Abstract. We investigate the Penrose limits of classical string and Mtheory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS ×S spacetimes and of supergravity brane solutions. We also present the Penrose limits of various other solutions: intersecting branes, supersymmetric black holes and strings in diverse dimensions, and cosmological models. We explore the Penrose limit of an isometrically embedded spacetime and find a generalisation to spaces with more than one time. Finally, we show that the Penrose limit is a large tension limit for all branes including those with fields of Born-Infeld type.

Gödel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

“…To take the Penrose limit along any of the above geodesics (parametrised by P ), we change coordinates from x µ = (r, z, φ, t) to adapted coordinates [13,15,17] (u, v, y 1 , y 2 ) with u = τ . A possible choice is r = r(u)…”

“…We can deal with the second term in the standard way [15,17], introducing 14) and shifting v appropriately to eliminate the dudx 2 cross-term. This will have the net effect of generating dx 2 2 − 4x 2 2 du 2 .…”

“…To take the Penrose limit of these Gödel metrics along any of the above geodesics, we go to adapted coordinates [13,15,17], i.e. we seek a change of coordinates from x µ = (r, z, φ, t) to (u, v, y 1 , y 2 ) with u = τ in such a way that g uv = 1 and g uu = g u1 = g u2 = 0.…”

PP-waves from rotating and continuously distributed D3-branes

“…For completeness we present here also the general form of a particular change of coordinates that is important for taking the Penrose limit (see also [26])…”

Type-IIB colliding plane waves

“…Indeed, these ansätze are appropriate for incoming BFHP waves in type-IIB supergravity [26] (or their analogues in lower dimension), which preserve an SO(n) × SO(n) symmetry. Here M, U, V, H 1 and H 2 are all functions of u and v only.…”