Holographic Description of M-branes via AdS$_2$

TL;DR

This work constructs explicit AdS$_2$/CFT$_1$ realizations with eight supercharges in controlled string-theory setups, focusing on non-compact internal geometries that require a UV completion. By analyzing both D1–NS5–D3 and D0–F1 intersections, the authors connect IR descriptions as quantum mechanical systems to UV completions in higher-dimensional CFTs: longitudinal M5-branes with momentum/NUT charges yield a 6d $(2,0)$ CFT UV completion, while longitudinal M2-branes provide a 3d M2 theory UV completion. Holographic free energies exhibit divergences due to non-compact directions, which are regularized by cutoffs and interpreted in terms of deconstructed extra dimensions; the IR dynamics consistently reduce to D0 QM descriptions with $F_{ m hol} \sim k^2$, while UV limits reproduce the expected higher-dimensional $N^3$-type scalings. The work also explores a non-Abelian T-dual route to linear-quiver quantum mechanics and its analytic continuation to AdS$_4$-type backgrounds, suggesting a broader network of AdS$_2$/CFT$_1$ dualities connected to higher-dimensional CFTs. Overall, the results provide explicit UV completions for non-compact AdS$_2$ holography via deconstruction and illuminate how M-brane momentum and NUT charges shape the IR/UV structure of these dualities.

Abstract

We study $\textrm{AdS}_2\times S^4 \times S^2 \times Σ_2$ 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 $\textrm{AdS}_2$ 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.

Figures (6)

• Figure 1: Annulus associated to the solution.
• Figure 2: Quiver describing the D0-D4 brane system.
• Figure 3: Circular quiver describing longitudinal M5-branes with momentum charge probing an ALE singularity.
• Figure 4: Infinite strip associated to the NATD solution.
• Figure 5: Brane set-up underlying the non-Abelian T-dual solution. The D3-branes are wrapped on $S^2$, such that the effective field theory living in them is one dimensional at low energies.