G/H M-branes and AdS_{p+2} Geometries

TL;DR

This work identifies a class of BPS M-branes—G/H branes—that correspond one-to-one with Freund–Rubin AdS_4 × G/H and AdS_7 × G/H vacua, where G/H are Einstein cosets with Killing spinors. Using a solvable Lie algebra parametrization of AdS_{p+2}, the authors construct explicit interpolating solutions whose near-horizon geometry is AdS_{p+2} × G/H and demonstrate how AdS isometries induce world-volume (super)conformal symmetries, including Maldacena-style broken conformal transformations. They provide detailed derivations of the p-brane action generalization, Vielbein, spin connection, Ricci tensor, and field equations for the G/H ansatz, and they compute Killing spinors in D=11 to show the preserved supersymmetry is 2N_{G/H} (M2) or 4N_{G/H} (M5), governed by the Killing spinors of the Freund–Rubin vacuum. The AdS_4 solvable parametrization yields the Bertotti–Robinson form and makes the relation between AdS isometries and world-volume conformal transformations explicit, offering a pathway to prospective microscopic world-volume theories and generalized compactifications.

Abstract

We prove the existence of a new class of BPS saturated M-branes. They are in one-to-one correspondence with the Freund--Rubin compactifications of M-theory on either (AdS_4) x (G/H) or (AdS_7) x (G/H), where G/H is the seven (or four) dimensional Einstein coset manifolds classified long ago in the context of Kaluza Klein supergravity. The G/H M-branes are solitons that interpolate between flat space at infinity and the old Kaluza-Klein compactifications at the horizon. They preserve N/2 supersymmetries where N is the number of Killing spinors of the (AdS) x (G/H) vacuum. A crucial ingredient in our discussion is the identification of a solvable Lie algebra parametrization of the Lorentzian non compact coset SO(2,p+1)/SO(1,p+1) corresponding to anti de Sitter space AdS_{p+2} . The solvable coordinates are those naturally emerging from the near horizon limit of the G/H p-brane and correspond to the Bertotti Robinson form of the anti-de-Sitter metric. The pull-back of anti-de-Sitter isometries on the p-brane world-volume contain, in particular, the broken conformal transformations recently found in the literature.