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F-theory and AdS_3/CFT_2 (2,0)

Christopher Couzens, Dario Martelli, Sakura Schafer-Nameki

TL;DR

The paper extends the AdS3/CFT2 dictionary to F-theory by allowing a spacetime varying axio-dilaton τ, deriving the general Type IIB conditions for AdS3 solutions with five-form flux and holomorphic τ, and identifying two main classes of solutions. It constructs new N=(0,2) AdS3 solutions with varying τ, including universal twist and baryonic twist sectors, and computes holographic central charges that match field theory expectations from twisted reductions of 4d N=1 theories. Additionally, when τ varies and the internal space decompactifies, the authors classify the most general AdS5 solutions with varying τ dual to 4d N=1 SCFTs and discuss dual M-theory AdS2 solutions, establishing a coherent web of dualities across IIB/F-theory, M-theory, and field theory via anomaly inflow and c-extremization. The results illuminate how τ variation and duality twists modify holographic data, including leading and subleading central charges and R/baryonic charges, and suggest intriguing connections to Yp,q and K3^τ geometries as well as non-compact F-theory compactifications with potential applications to 4d/2d and 2d/1d holography. The work lays groundwork for rigorous treatment of varying coupling field theories and motivates further exploration of subleading contributions from 7-brane sectors and deeper M-theory realizations.

Abstract

We continue to develop the program initiated in arXiv:1705.04679 of studying supersymmetric AdS_3 solutions of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of 4d theories with varying coupling. Imposing 2d N=(0,2) supersymmetry, we derive the general conditions on the geometry for Type IIB AdS_3 solutions with varying axio-dilaton and five-form flux. We discuss a class of solutions, which extend AdS_3 x T^2 x M_5 Type IIB backgrounds, to F-theory geometries of the type AdS_3 x K3 x M_5 with varying axio-dilaton characterizing the elliptic fiber of the K3, and describe their dual field theories. For a specific choice of M_5 this corresponds to a family of solutions that are conjectured to be dual to twisted compactifications of 4d N=1 Y^{p,q} quiver gauge theories on a curve with varying coupling. For this setup, we compare the central charges from holography and field theory and find agreement to subleading order in N. Requiring enhanced 2d N=(2,2) supersymmetry we find that the axio-dilaton must be constant. However, if the internal geometry is allowed to be non-compact, we obtain the most general class of Type IIB AdS_5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N=1 SCFTs.

F-theory and AdS_3/CFT_2 (2,0)

TL;DR

The paper extends the AdS3/CFT2 dictionary to F-theory by allowing a spacetime varying axio-dilaton τ, deriving the general Type IIB conditions for AdS3 solutions with five-form flux and holomorphic τ, and identifying two main classes of solutions. It constructs new N=(0,2) AdS3 solutions with varying τ, including universal twist and baryonic twist sectors, and computes holographic central charges that match field theory expectations from twisted reductions of 4d N=1 theories. Additionally, when τ varies and the internal space decompactifies, the authors classify the most general AdS5 solutions with varying τ dual to 4d N=1 SCFTs and discuss dual M-theory AdS2 solutions, establishing a coherent web of dualities across IIB/F-theory, M-theory, and field theory via anomaly inflow and c-extremization. The results illuminate how τ variation and duality twists modify holographic data, including leading and subleading central charges and R/baryonic charges, and suggest intriguing connections to Yp,q and K3^τ geometries as well as non-compact F-theory compactifications with potential applications to 4d/2d and 2d/1d holography. The work lays groundwork for rigorous treatment of varying coupling field theories and motivates further exploration of subleading contributions from 7-brane sectors and deeper M-theory realizations.

Abstract

We continue to develop the program initiated in arXiv:1705.04679 of studying supersymmetric AdS_3 solutions of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of 4d theories with varying coupling. Imposing 2d N=(0,2) supersymmetry, we derive the general conditions on the geometry for Type IIB AdS_3 solutions with varying axio-dilaton and five-form flux. We discuss a class of solutions, which extend AdS_3 x T^2 x M_5 Type IIB backgrounds, to F-theory geometries of the type AdS_3 x K3 x M_5 with varying axio-dilaton characterizing the elliptic fiber of the K3, and describe their dual field theories. For a specific choice of M_5 this corresponds to a family of solutions that are conjectured to be dual to twisted compactifications of 4d N=1 Y^{p,q} quiver gauge theories on a curve with varying coupling. For this setup, we compare the central charges from holography and field theory and find agreement to subleading order in N. Requiring enhanced 2d N=(2,2) supersymmetry we find that the axio-dilaton must be constant. However, if the internal geometry is allowed to be non-compact, we obtain the most general class of Type IIB AdS_5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N=1 SCFTs.

Paper Structure

This paper contains 68 sections, 447 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. $\hbox{AdS}_3$ Solutions in F-theory dual to 2d $\mathcal{N}=(0,2)$
  3. Killing Spinor Equations
  4. AdS$_{3}$ Ansatz and $(0,2)$ Supersymmetry
  5. Constraints on the Geometry
  6. Sufficiency of the Conditions
  7. Equations of Motion
  8. Supersymmetry
  9. Summary of Conditions
  10. F-theoretic Formulation
  11. $\hbox{AdS}_3$ with 2d $\mathcal{N}=(2,2)$ and $\hbox{AdS}_5$ with Varying $\tau$
  12. Torsion Conditions
  13. Constant $\tau$: $\hbox{AdS}_3$ Duals to $\mathcal{N}=(2,2)$
  14. Varying $\tau$: $\hbox{AdS}_5$ Duals to 4d $\mathcal{N}=1$
  15. New $\mathcal{N}=(0,2)$ Solutions with Varying $\tau$
  16. ...and 53 more sections

Figures (3)

  • Figure 1: Toric diagram for $\mathfrak{Y}^{\mathfrak{p},\mathfrak{q}}$. Notice that this is not convex, however the external lines do not intersect. The figure is representative of the choice $\mathfrak{p}=3$, $\mathfrak{q}=4$.
  • Figure 2: Toric diagram for $Y^{p,q}$. The figure is representative of the choice $p=4$ and $q=3$.
  • Figure 3: The $Y^{4,3}$ quiver diagram. The quiver diagram for $Y^{4,3}$. The fields have been colour-coded as follows: the $Y$ fields are shown in blue, $Z$ fields in red, $U_{i}$ fields are purple and $V_{i}$ fields green.