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Generalised supersymmetric fluxbranes

José Figueroa-O'Farrill, Joan Simón

TL;DR

This work classifies generalised supersymmetric fluxbranes in type II string theory as Kaluza–Klein reductions of the $11$-dimensional Minkowski vacuum, revealing two main families distinguished by their Lorentz data and yielding explicit, smooth backgrounds that include known fluxbranes, novel nullbranes, and interpolating solutions. By formulating the reductions in terms of a nilpotent plus rotation or pure rotations with constrained rotation parameters, the authors derive concrete warp-factor and RR-field expressions and map out the resulting spectrum of elementary objects ($F5$, $F3$, $F1$, $N7$) and their interpolations. The paper further develops a comprehensive network of U-dualities, using a consistent notation for $(p,q)$-brane configurations and showing how T-, S-dualities and M-theory uplifts connect fluxbranes, fluxstrings, and nullbranes across IIA/IIB. These results provide a robust framework for constructing explicit supersymmetric backgrounds and exploring their brane-intersection physics and potential field-theory duals in decoupling limits.

Abstract

We classify generalised supersymmetric fluxbranes in type II string theory obtained as Kaluza-Klein reductions of the Minkowski space vacuum of eleven-dimensional supergravity. We obtain two families of smooth solutions which contains all the known solutions, new solutions called nullbranes, and solutions interpolating between them. We explicitly construct all the solutions and we study the U-duality orbits of some of these backgrounds.

Generalised supersymmetric fluxbranes

TL;DR

This work classifies generalised supersymmetric fluxbranes in type II string theory as Kaluza–Klein reductions of the -dimensional Minkowski vacuum, revealing two main families distinguished by their Lorentz data and yielding explicit, smooth backgrounds that include known fluxbranes, novel nullbranes, and interpolating solutions. By formulating the reductions in terms of a nilpotent plus rotation or pure rotations with constrained rotation parameters, the authors derive concrete warp-factor and RR-field expressions and map out the resulting spectrum of elementary objects (, , , ) and their interpolations. The paper further develops a comprehensive network of U-dualities, using a consistent notation for -brane configurations and showing how T-, S-dualities and M-theory uplifts connect fluxbranes, fluxstrings, and nullbranes across IIA/IIB. These results provide a robust framework for constructing explicit supersymmetric backgrounds and exploring their brane-intersection physics and potential field-theory duals in decoupling limits.

Abstract

We classify generalised supersymmetric fluxbranes in type II string theory obtained as Kaluza-Klein reductions of the Minkowski space vacuum of eleven-dimensional supergravity. We obtain two families of smooth solutions which contains all the known solutions, new solutions called nullbranes, and solutions interpolating between them. We explicitly construct all the solutions and we study the U-duality orbits of some of these backgrounds.

Paper Structure

This paper contains 17 sections, 93 equations, 3 figures.

Table of Contents

  1. Introduction and conclusions
  2. Kaluza--Klein reduction and generalised fluxbranes
  3. The geometrical setting
  4. Classification of smooth supersymmetric fluxbranes
  5. Generalised supersymmetric fluxbranes
  6. Supersymmetric fluxbranes
  7. The supersymmetric F5-brane revisited
  8. The supersymmetric F3-brane
  9. Supersymmetric fluxstrings
  10. Supersymmetric nullbranes
  11. Generalised supersymmetric fluxbranes
  12. Dualities and flux branes
  13. A word on the notation
  14. F5-brane dualities
  15. F3-brane dualities
  16. ...and 2 more sections

Figures (3)

  • Figure 1: Web of dualities associated with an F5-brane. A dotted line represents an S-duality transformation, a unidirectional solid line represents a Kaluza--Klein reduction from M-theory, and a bidirectional solid line a T-duality transformation.
  • Figure 2: Web of dualities associated with an F3-brane. A dotted line represents an S-duality transformation, a unidirectional solid line represents a Kaluza--Klein reduction from M-theory, and a bidirectional solid line a T-duality transformation.
  • Figure 3: Web of dualities associated with a F1-string. A bold line represents an S-duality transformation, while unidirectional lines indicate Kaluza--Klein reductions from M-theory, and bidirectional lines a T-duality transformation. This diagram is valid for both types of fluxstrings, adding the relevant subscript ($1$ or $2$, but always the same) to the $F(0,1)$ solutions.