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On $\text{AdS}_2\times \text{S}^7$, its $\mathbb{Z}_k$ orbifold and their dual quantum mechanics

Yolanda Lozano, Niall T. Macpherson, Achilleas Passias

TL;DR

This paper extends AdS$_2$ holography by constructing new AdS$_2$ backgrounds in massive IIA with $S^7$ replaced by $S^7/\mathbb{Z}_k$, yielding ${\cal N}=6$ globally and enabling compact internal spaces through interior D8-branes. It then derives a Type IIB dual class, AdS$_2\times\mathbb{CP}^3\times S^1\times I$, and connects massless limits to AdS$_4/\mathbb{Z}_{k'}\times S^7/\mathbb{Z}_k$ via a web of dualities, clarifying the underlying brane configurations. The authors propose dual 1d SCQMs realized on D0–F1–D8 intersections, represented as disconnected quivers, and discuss a baryon-vertex interpretation for these geometries. Together, these results outline a rich duality network linking ABJM/M2-brane setups to AdS$_2$ geometries and provide a framework for holographic central-charge analyses, while leaving open precise matching between holographic and field-theoretic central charges and suggesting multiple future directions (fractional branes, deformations, and higher-supersymmetry extensions).

Abstract

We consider a previously constructed class of massive Type IIA AdS$_2\times$S$^7\times I$ solutions with OSp$(8|2)$ symmetry, as well as OSp$(6|2)$-symmetric ones, by replacing the S$^7$ with the orbifold S$^7/\mathbb{Z}_k$. In both cases we construct global solutions for which the interval $I$ is bounded between physical singularities, by allowing D8-branes transverse to $I$. We also generate a new class of Type IIB AdS$_2\times \mathbb{CP}^3\times\text{S}^1\times I$ solutions by T-duality and establish a chain of dualities that maps the massless limit of these classes to AdS$_4/\mathbb{Z}_{k'}\times\text{S}^7/\mathbb{Z}_k$, thus identifying the brane configurations yielding these solutions. We propose that the ${\cal N}=8$ solutions are dual to a theory living on a D0-F1-D8 brane intersection which has a description in terms of disconnected quivers and similarly for the ${\cal N}=6$ solutions.

On $\text{AdS}_2\times \text{S}^7$, its $\mathbb{Z}_k$ orbifold and their dual quantum mechanics

TL;DR

This paper extends AdS holography by constructing new AdS backgrounds in massive IIA with replaced by , yielding globally and enabling compact internal spaces through interior D8-branes. It then derives a Type IIB dual class, AdS, and connects massless limits to AdS via a web of dualities, clarifying the underlying brane configurations. The authors propose dual 1d SCQMs realized on D0–F1–D8 intersections, represented as disconnected quivers, and discuss a baryon-vertex interpretation for these geometries. Together, these results outline a rich duality network linking ABJM/M2-brane setups to AdS geometries and provide a framework for holographic central-charge analyses, while leaving open precise matching between holographic and field-theoretic central charges and suggesting multiple future directions (fractional branes, deformations, and higher-supersymmetry extensions).

Abstract

We consider a previously constructed class of massive Type IIA AdSS solutions with OSp symmetry, as well as OSp-symmetric ones, by replacing the S with the orbifold S. In both cases we construct global solutions for which the interval is bounded between physical singularities, by allowing D8-branes transverse to . We also generate a new class of Type IIB AdS solutions by T-duality and establish a chain of dualities that maps the massless limit of these classes to AdS, thus identifying the brane configurations yielding these solutions. We propose that the solutions are dual to a theory living on a D0-F1-D8 brane intersection which has a description in terms of disconnected quivers and similarly for the solutions.

Paper Structure

This paper contains 12 sections, 53 equations, 9 figures, 11 tables.

Table of Contents

  1. Introduction
  2. $\text{AdS}_2\times\text{S}^7/\mathbb{Z}_k \times I$ with $\mathcal{N}=6$ in massive Type IIA
  3. Physical boundary behaviours
  4. Global Solutions
  5. A new class of $\text{AdS}_2\times \mathbb{CP}^3\times \text{S}^1\times I$ solutions to Type IIB with $\mathcal{N}=6$ supersymmetry
  6. Massless limit. Connection to the solutions in Conti:2023rul
  7. Field theory interpretation of the $\mathcal{N}=8$ solutions
  8. Quiver quantum mechanics and central charge
  9. Field theory interpretation of the $\mathcal{N}=6$ solutions
  10. M2-branes on $\mathbb{C}^4/\mathbb{Z}_k$ with momentum as a brane box
  11. Adding D6-branes
  12. Conclusions

Figures (9)

  • Figure 1: Web of dualities that relate the new AdS$_2$ solution constructed in section \ref{['sec:N=6']} (on the left-hand side) with the solution constructed in Conti:2023rul corresponding to zero Romans mass (on the right-hand side).
  • Figure 2: F1-strings stretched between D0 and D8-branes.
  • Figure 3: Hanany-Witten like brane set-up associated to the quantised charges of the $\mathcal{N}=8$ solutions.
  • Figure 4: Hanany-Witten like brane set-up equivalent to the configuration in Figure \ref{['D0-F1-D8branes']}.
  • Figure 5: Disconnected quivers describing the superconformal quantum mechanics dual to the solutions \ref{['metric']}-\ref{['RR1']} for $k=1$. Circles denote $\mathcal{N}=8$ vector multiplets, black lines $\mathcal{N}=8$ hypermultiplets and grey dashed lines $\mathcal{N}=2$ Fermi multiplets.
  • ...and 4 more figures