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N=2 Supersymmetry and de Sitter space

Renata Kallosh

TL;DR

This work demonstrates a unique avenue for de Sitter solutions within N=2 supersymmetry by constructing a hybrid hypersymmetry model with a vector multiplet and a charged hypermultiplet, augmented by a Fayet-Iliopoulos term that softly breaks the SU(2,2|2) superconformal symmetry. The resulting potential exhibits a slow-roll de Sitter phase with spontaneously broken SUSY, followed by a rapid waterfall to a ground state with two unbroken SUSY charges and zero cosmological constant, achieved through a hypersymmetric Higgs mechanism. The authors embed this construction within the broader N=2 gauged supergravity framework, discuss obstructions to coupling FI terms to N=2 SUGRA, and show compatibility with N=1 supergravity, yielding a P-term inflation scenario and potential relevance to the current cosmic acceleration. The model links N=2 cosmology with superconformal structure and hints at connections to string theory via AdS$_5$ boundaries, offering a restrained yet predictive alternative to traditional N=1 inflationary setups.

Abstract

We present a (unique?) possibility of de Sitter solution in the framework of N=2 supersymmetry (hypersymmetry). We show that a model with a vector and a charged hypermultiplet has a hybrid inflation type potential. It leads to a slow-roll regime in de Sitter type background with all supersymmetries broken spontaneously. Beyond the bifurcation point the waterfall stage abruptly brings the system into a ground state with 2 unbroken supersymmetries. De Sitter stage exists under condition that the superconformal SU(2,2|2) symmetry of the model is softly broken down to N=2 supersymmetry by the vev of the Killing prepotential triplet P^r. This hybrid hypersymmetry model may describe P-term inflation and/or acceleration of the universe at the present epoch.

N=2 Supersymmetry and de Sitter space

TL;DR

This work demonstrates a unique avenue for de Sitter solutions within N=2 supersymmetry by constructing a hybrid hypersymmetry model with a vector multiplet and a charged hypermultiplet, augmented by a Fayet-Iliopoulos term that softly breaks the SU(2,2|2) superconformal symmetry. The resulting potential exhibits a slow-roll de Sitter phase with spontaneously broken SUSY, followed by a rapid waterfall to a ground state with two unbroken SUSY charges and zero cosmological constant, achieved through a hypersymmetric Higgs mechanism. The authors embed this construction within the broader N=2 gauged supergravity framework, discuss obstructions to coupling FI terms to N=2 SUGRA, and show compatibility with N=1 supergravity, yielding a P-term inflation scenario and potential relevance to the current cosmic acceleration. The model links N=2 cosmology with superconformal structure and hints at connections to string theory via AdS boundaries, offering a restrained yet predictive alternative to traditional N=1 inflationary setups.

Abstract

We present a (unique?) possibility of de Sitter solution in the framework of N=2 supersymmetry (hypersymmetry). We show that a model with a vector and a charged hypermultiplet has a hybrid inflation type potential. It leads to a slow-roll regime in de Sitter type background with all supersymmetries broken spontaneously. Beyond the bifurcation point the waterfall stage abruptly brings the system into a ground state with 2 unbroken supersymmetries. De Sitter stage exists under condition that the superconformal SU(2,2|2) symmetry of the model is softly broken down to N=2 supersymmetry by the vev of the Killing prepotential triplet P^r. This hybrid hypersymmetry model may describe P-term inflation and/or acceleration of the universe at the present epoch.

Paper Structure

This paper contains 12 sections, 53 equations, 5 figures.

Table of Contents

  1. Introduction
  2. De Sitter solutions in N=1 supergravity
  3. Hybrid hypersymmetry model
  4. $SU(2,2|2)$ superconformal part of the model
  5. N=2 supersymmetry after soft breaking of superconformal symmetry
  6. Hybrid hypersymmetry model as an example of generic N=2 gauge theory
  7. Vacua of the hybrid hypersymmetry model
  8. Coupling gauge theories to supergravity
  9. Potentials of N=2 gauged supergravities
  10. FI terms and topological obstruction to couple hybrid hypersymmetry model to N=2 supergravity
  11. Coupling of hybrid hypersymmetry model to N=1 supergravity
  12. P-term inflation and acceleration of the universe

Figures (5)

  • Figure 1: The potential of the hybrid hypersymmetry model. After a long de Sitter stage a local valley at $x=0$, $y\geq y_b$ is replaced by a waterfall stage at $x=0$, $0\leq y_b$ .
  • Figure 2: The potential close to the bifurcation point $x=0$, $y=y_b= 1/\sqrt 2$.
  • Figure 3: The potential is flat at the bifurcation point and has a maximum at $x=0$ and $y<y_b$.
  • Figure 4: The potential beyond the bifurcation point shows a local maximum de Sitter stage, extremely unstable. The absolute ground state at $y=0$, $x^2= 1$ has 2 unbroken supersymmetries.
  • Figure 5: Slices of the potential of the hybrid hypersymmetric model, from $y = 0$ to $y = 10$. The lower curve corresponds to $y= 0$. The curvature becomes positive for $y > 1/\sqrt 2$.