Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Type IIA geometries dual to N = 2 SCFTs

R. A. Reid-Edwards, B. Stefanski

TL;DR

The paper achieves explicit Type IIA supergravity backgrounds with AdS5 factors that are conjectured to be dual to general N=2 SCFTs by solving the GM Toda/Laplace system under appropriate boundary conditions. It develops a systematic framework to construct solutions from Maldacena–Nunez building blocks, introducing Uluru-type periodic profiles and showing how general non-periodic and periodic profiles decompose into MN contributions. The results provide concrete geometric and holographic data (metric, dilaton, fluxes) tied to generalized quivers, and analyze the large-ρ behavior revealing regimes where perturbative string theory applies versus when a full M-theory description is necessary. The work also clarifies the role of smearing in the GM reduction and outlines future directions toward non-smeared, fully local Toda solutions for complete dual descriptions.

Abstract

We provide explicit solutions of Type IIA supergravity which are believed to be dual to N = 2 superconformal four dimensional gauge theories. These explicit solutions are based on the general ansatz for such a type of backgrounds introduced by Gaiotto and Maldacena.

On Type IIA geometries dual to N = 2 SCFTs

TL;DR

The paper achieves explicit Type IIA supergravity backgrounds with AdS5 factors that are conjectured to be dual to general N=2 SCFTs by solving the GM Toda/Laplace system under appropriate boundary conditions. It develops a systematic framework to construct solutions from Maldacena–Nunez building blocks, introducing Uluru-type periodic profiles and showing how general non-periodic and periodic profiles decompose into MN contributions. The results provide concrete geometric and holographic data (metric, dilaton, fluxes) tied to generalized quivers, and analyze the large-ρ behavior revealing regimes where perturbative string theory applies versus when a full M-theory description is necessary. The work also clarifies the role of smearing in the GM reduction and outlines future directions toward non-smeared, fully local Toda solutions for complete dual descriptions.

Abstract

We provide explicit solutions of Type IIA supergravity which are believed to be dual to N = 2 superconformal four dimensional gauge theories. These explicit solutions are based on the general ansatz for such a type of backgrounds introduced by Gaiotto and Maldacena.

Paper Structure

This paper contains 21 sections, 86 equations, 10 figures.

Table of Contents

  1. Introduction
  2. A review of the GM solutions
  3. The GM solution
  4. The GM boundary conditions
  5. Consistent $\lambda$ profiles
  6. Infinite conducting disc
  7. Metric Positivity Constraints
  8. Dual gauge theory
  9. GM spacetimes on the hyperbolic plane
  10. Changing variables
  11. The Maldacena-Nunez solution
  12. General Non-periodic Solution
  13. Uluru spacetimes
  14. A simple Uluru spacetime
  15. General Periodic Solution
  16. ...and 6 more sections

Figures (10)

  • Figure 1: The two types of line charge; the MN-type (left) and the Uluru-type (right)
  • Figure 2: Two ways of viewing the boundary condition
  • Figure 3: There is a correspondence between the quiver diagram and the line charge. The integers $k_I\in\mathbb{Z}_+$ are the change in the gradient at the kink, given by $k_I=a_{I-1}-a_I$, where $a_I$ is the gradient of the $I$'th line element. Note that $\eta_I,n_I\in\mathbb{Z}_+$.
  • Figure 4: The MN line charge density profile
  • Figure 5: $\dot{V}$ for the MN solution
  • ...and 5 more figures