Spacetimes of Boosted p-branes, and CFT in Infinite-momentum Frame

TL;DR

This work generalises the AdS/CFT correspondence to spacetimes obtained from extremal p-branes endowed with world-volume pp-waves, showing that their near-horizon geometries are Kaigorodov-type $K_n$ metrics rather than AdS$_n$ and that a fixed momentum density governs the gravity-decoupling limit. By performing dimensional reductions, the authors map these boosted brane configurations to two-charge black holes in various dimensions and provide a boosted-dilute gas picture that microscopically accounts for their entropy in the near-extremal regime. The results extend to M5- and D3-branes, yielding higher-dimensional CNH metrics as non-extremal reductions and revealing a consistent picture where the boundary CFT lives in an infinite-momentum frame with constant momentum density. Collectively, the paper proposes a coherent framework connecting Kaigorodov-type bulk geometries to CFTs in boosted frames, with clear implications for microstate counting and entropy in boosted two-charge black holes.

Abstract

We study the spacetimes of the near-horizon regions in D3-brane, M2-brane and M5-brane configurations, in cases where there is a pp-wave propagating along a direction in the world-volume. While non-extremal configurations of this kind locally have the same Carter-Novotny-Horsky-type metrics as those without the wave, taking the BPS limit results instead in Kaigorodov-type metrics, which are homogeneous, but preserve 1/4 of the supersymmetry, and have global and local structures that are quite different from the corresponding anti-de Sitter spacetimes associated with solutions where there is no pp-wave. We show that the momentum density of the system is non-vanishing and held fixed under the gravity decoupling limit. In view of the AdS/CFT correspondence, M-theory and type IIB theory in the near-horizon region of these boosted BPS-configurations specifies the corresponding CFT on the boundary in an infinitely-boosted frame with constant momentum density. We model the microstates of such boosted configurations (which account for the microscopic counting of near-extremal black holes in D=7, D=9 and D=6) by those of a boosted dilute massless gas in a d=4, d=3 and d=6 spacetime respectively. Thus we obtain a simple description for the entropy of 2-charge black holes in D=7,9 and 6 dimensions. The paper includes constructions of generalisations of the Kaigorodov and Carter-Novotny-Horsky metrics in arbitrary spacetime dimensions, and an investigation of their properties.