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$\text{AdS}_2\times \text{S}^2\times \text{CY}_2$ solutions in Type IIB with 8 supersymmetries

Yolanda Lozano, Carlos Nunez, Anayeli Ramirez

TL;DR

This work constructs two infinite families of AdS$_2$-preserving Type IIB backgrounds with eight supercharges: a local AdS$_2\times$S$^2\times$CY$_2\times$S$^1$ geometry fibered over an interval (plus connections to CGK via annulus limits) and a cohomogeneity-two family obtained by non-Abelian T-duality, yielding an infinite-strip CGK embedding. It analyzes brane content (D1/D5 colour branes, D3/D7 flavour branes, NS5/F1), computes the holographic central charge for the dual one-dimensional conformal quantum mechanics, and establishes an electric–magnetic RR flux correspondence that ties NS-NS data to RR data. A phenomenological extremisation principle is proposed via a functional ${\mathcal{C}}$ of RR fluxes whose minimisation reproduces the central charge, suggesting a unified RR/NSNS holographic framework for AdS$_2$ systems. The results illuminate the landscape of AdS$_2$ holography, connect the new solutions to CGK geometries, and open avenues for global completion, integrability questions, and extensions to other dimensions.

Abstract

We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is $\text{AdS}_2\times\text{S}^2\times \text{CY}_2\times \text{S}^1$ fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in \cite{Lozano:2020txg}. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of $\text{AdS}_2\times \text{S}^2\times \text{CY}_2$ solutions fibered over a 2d Riemann surface $Σ$ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D'Hoker and Gutperle for $Σ$ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

$\text{AdS}_2\times \text{S}^2\times \text{CY}_2$ solutions in Type IIB with 8 supersymmetries

TL;DR

This work constructs two infinite families of AdS-preserving Type IIB backgrounds with eight supercharges: a local AdSSCYS geometry fibered over an interval (plus connections to CGK via annulus limits) and a cohomogeneity-two family obtained by non-Abelian T-duality, yielding an infinite-strip CGK embedding. It analyzes brane content (D1/D5 colour branes, D3/D7 flavour branes, NS5/F1), computes the holographic central charge for the dual one-dimensional conformal quantum mechanics, and establishes an electric–magnetic RR flux correspondence that ties NS-NS data to RR data. A phenomenological extremisation principle is proposed via a functional of RR fluxes whose minimisation reproduces the central charge, suggesting a unified RR/NSNS holographic framework for AdS systems. The results illuminate the landscape of AdS holography, connect the new solutions to CGK geometries, and open avenues for global completion, integrability questions, and extensions to other dimensions.

Abstract

We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in \cite{Lozano:2020txg}. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of solutions fibered over a 2d Riemann surface constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D'Hoker and Gutperle for an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

Paper Structure

This paper contains 18 sections, 84 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. New AdS$_2\times \text{S}^2\times \text{CY}_2$ backgrounds
  3. Brane charges and brane set-up
  4. Holographic central charge
  5. Aspects of the dual Conformal Quantum Mechanics
  6. Connection with the $\text{AdS}_2\times \text{S}^2\times \text{CY}_2\times \Sigma$ backgrounds of Chiodaroli-Gutperle-Krym
  7. Review of the CGK geometries
  8. Our AdS$_2$ geometries and the "plus-solution"
  9. The LNRS geometries and the "minus-solution"
  10. The annulus
  11. Zoom-in to our solutions
  12. A new class of AdS$_2\times \text{S}^2\times \text{CY}_2\times \Sigma$ solutions with $\Sigma$ an infinite strip
  13. NATD of the AdS$_3\times$S$^2\times$CY$_2$ solutions
  14. The NATD solution as a CGK geometry
  15. Electric-magnetic charges and a minimisation principle
  16. ...and 3 more sections

Figures (4)

  • Figure 1: Relations between the infinite family of AdS$_3$ backgrounds to massive IIA constructed in Lozano:2019emq (top left), the IIB AdS$_2$ backgrounds studied in Lozano:2020txg (bottom left), the IIA AdS$_2$ backgrounds constructed in Lozano:2020sae (top right), and the new AdS$_2$ solutions in Type IIB given by eqs.(\ref{['NS sector-B']})-(\ref{['RR sector lower rank fluxes']}) (bottom right).
  • Figure 2: The proposed quantum mechanical quiver. This follows from the analysis of open strings in the Hanany-Witten set-up.
  • Figure 3: Riemann surface associated to our AdS$_2$ geometries. Given the periodicity of $\psi$ it defines an annulus.
  • Figure 4: Infinite strip associated to the NATD solution.