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Supersymmetric AdS_5 solutions of massive IIA supergravity

Fabio Apruzzi, Marco Fazzi, Achilleas Passias, Alessandro Tomasiello

TL;DR

This paper classifies supersymmetric AdS5 solutions in massive IIA, motivated by AdS7 backgrounds, by reducing the problem to a PDE system that determines the internal M5 geometry as a fibration over a surface. An Ansatz linking the base to the warp factor simplifies the PDEs to ODEs, yielding a complete analytic set that includes a new regular AdS5 family; these solutions map universally to AdS7 backgrounds, implying that the dual CFT4s arise from twisted compactifications of the 6d (1,0) CFTs. The authors derive explicit AdS7 expressions via this map and compute central charges and free energies in simple flux configurations, finding cubic dependences on flux quanta. The work establishes a robust framework for connecting 4d N=1 SCFTs to 6d (1,0) theories through twisted compactifications on Riemann surfaces, and provides analytic gravity solutions that can serve as a starting point for further field-theory interpretations and holographic checks.

Abstract

Motivated by a recently found class of AdS_7 solutions, we classify AdS_5 solutions in massive IIA, finding infinitely many new analytical examples. We reduce the general problem to a set of PDEs, determining the local internal metric, which is a fibration over a surface. Under a certain simplifying assumption, we are then able to analytically solve the PDEs and give a complete list of all solutions. Among these, one class is new and regular. These spaces can be related to the AdS_7 solutions via a simple universal map for the metric, dilaton and fluxes. The natural interpretation of this map is that the dual CFT_6 and CFT_4 are related by twisted compactification on a Riemann surface $Σ_g$. The ratio of their free energy coefficients is proportional to the Euler characteristic of $Σ_g$. As a byproduct, we also find the analytic expression for the AdS_7 solutions, which were previously known only numerically. We determine the free energy for simple examples: it is a simple cubic function of the flux integers.

Supersymmetric AdS_5 solutions of massive IIA supergravity

TL;DR

This paper classifies supersymmetric AdS5 solutions in massive IIA, motivated by AdS7 backgrounds, by reducing the problem to a PDE system that determines the internal M5 geometry as a fibration over a surface. An Ansatz linking the base to the warp factor simplifies the PDEs to ODEs, yielding a complete analytic set that includes a new regular AdS5 family; these solutions map universally to AdS7 backgrounds, implying that the dual CFT4s arise from twisted compactifications of the 6d (1,0) CFTs. The authors derive explicit AdS7 expressions via this map and compute central charges and free energies in simple flux configurations, finding cubic dependences on flux quanta. The work establishes a robust framework for connecting 4d N=1 SCFTs to 6d (1,0) theories through twisted compactifications on Riemann surfaces, and provides analytic gravity solutions that can serve as a starting point for further field-theory interpretations and holographic checks.

Abstract

Motivated by a recently found class of AdS_7 solutions, we classify AdS_5 solutions in massive IIA, finding infinitely many new analytical examples. We reduce the general problem to a set of PDEs, determining the local internal metric, which is a fibration over a surface. Under a certain simplifying assumption, we are then able to analytically solve the PDEs and give a complete list of all solutions. Among these, one class is new and regular. These spaces can be related to the AdS_7 solutions via a simple universal map for the metric, dilaton and fluxes. The natural interpretation of this map is that the dual CFT_6 and CFT_4 are related by twisted compactification on a Riemann surface . The ratio of their free energy coefficients is proportional to the Euler characteristic of . As a byproduct, we also find the analytic expression for the AdS_7 solutions, which were previously known only numerically. We determine the free energy for simple examples: it is a simple cubic function of the flux integers.

Paper Structure

This paper contains 38 sections, 204 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The conditions for supersymmetry
  3. Mink(4) x M(6)
  4. AdS(5) x M(5)
  5. Parametrization of psi**1, psi**2 and the identity structure
  6. Analysis of the conditions for supersymmetry
  7. Geometry
  8. Fluxes
  9. Bianchi identities
  10. Summary so far
  11. A compactification Ansatz
  12. Simplifying the PDEs
  13. F(0) = 0
  14. F(0) != 0
  15. Generic case
  16. ...and 23 more sections

Figures (1)

  • Figure 1: Brane configurations for two sample theories. The circles represent stacks of $N$ NS5-branes; the horizontal lines represent D6-branes; the vertical lines represent D8-branes. In the second case, on each side we have $n_0=2$ D8-branes; $|\mu|=3$ D6-branes end on each, for a total of $k= n_0 |\mu|=6$.