Holographic description of M-branes via AdS2

Abstract

We study AdS 2 × S 4 × S 2 × Σ 2 solutions in type IIB string theory arising from D1 -D3 -NS5 brane intersections. These backgrounds enjoy sixteen supercharges and the corresponding internal geometry is non-compact due to the specific form of the warping w.r.t. the Riemann surface Σ 2 . Even though a direct computation of the holographic free energy of the would-be dual CFT 1 yields a divergent behaviour, it reveals the typical N 3 scaling of a 6d theory upon introducing a hard cut-off. We claim that such geometries may be interpreted as the gravity duals of M(atrix) models describing an IR phase of the (2, 0) theory of M5 branes, in presence of momentum and NUT charges. We discuss parallel AdS 2 geometries describing longitudinal M2 branes in the UV, where the counting of the number of degrees of freedom correctly reproduces the expected N 3/2 behaviour of the dual field theory. These geometries provide explicit examples where deconstructed extra dimensions yield well-defined UV descriptions in terms of higher-dimensional CFTs.

M -strings and AdS3 solutions to M-theory with small $$ \mathcal{N} $$ = (0, 4) supersymmetry

“…On the other hand, the relation between the action of M 5 -branes and the central charge indicates that these branes (that provide a boundary condition for the membranes to end) capture on their world-volumes the dynamics of the lower dimensional branes. This is a non-trivial fact, already encountered in [50]. It would be of interest to reproduce it in other holographic systems to fully understand its origin.…”

“…The results in [50] are particularly interesting regarding our system. Indeed, the system depicted in table 4 can be thought of as the result of adding F1-branes to the 1/4-BPS D0-D4 brane system discussed in [50], dual to a AdS 2 ×S 3 × S 4 geometry foliated over an interval. The D0-D4 brane system describes in M(atrix) theory longitudinal M5-branes, in terms of a U(k) gauge theory with hypermultiplets in the adjoint representation and N fundamentals [39].…”

“…Connections between AdS 2 solutions and M(atrix) theory have been discussed in the literature in various contexts (see for instance [50,[57][58][59][60]). The results in [50] are particularly interesting regarding our system. Indeed, the system depicted in table 4 can be thought of as the result of adding F1-branes to the 1/4-BPS D0-D4 brane system discussed in [50], dual to a AdS 2 ×S 3 × S 4 geometry foliated over an interval.…”

“…3 Alternatively, one could think of our system in terms of a 1/4-BPS D0-F1 brane system with extra D4-branes. 1/4-BPS D0-F1 branes are dual to a AdS 2 ×S 7 geometry foliated over an interval [50,61]. Our solutions can be interpreted in these set-ups as the fully backreacted supergravity solutions that arise when F1-strings are placed in the AdS 2 ×S 3 ×S 4 geometry dual to the D0-D4 brane system, or D4-branes are placed in the AdS 2 ×S 7 ×I solutions dual to the D0-F1 brane system, uplifted to eleven dimensions.…”

New AdS2 backgrounds and $$ \mathcal{N} $$ = 4 conformal quantum mechanics

“…A natural extension is the study of backgrounds with an AdS 2 factor [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. These should be dual to superconformal quantum mechanics (SCQM).…”