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Emergence of Spontaneously Broken Supersymmetry on an Anti-D3-Brane in KKLT dS Vacua

Renata Kallosh, Timm Wrase

TL;DR

The authors show that the KKLT uplifting term can be realized via spontaneous SUSY breaking on an anti-D3-brane, described by a nilpotent chiral multiplet with $S^2=0$ and a Volkov-Akulov goldstino. By imposing an O3 orientifold and a compatible κ-symmetry gauge, they demonstrate that the D3/anti-D3 world-volume actions reduce to Volkov-Akulov dynamics, yielding a 4D potential $V = V_{KKLT}( ho,ar{ ho}) + {M^4}/{( ho+ar{ ho})^3}$ with the anti-D3 providing the goldstino multiplet. The anti-D3-brane contributes a doubled VA term, while the D3-brane can cancel under the same projection, establishing a concrete string-theoretic mechanism for SUSY breaking and uplift in KKLT. This work connects brane-worldvolume physics to manifestly supersymmetric 4D supergravity with nilpotent multiplets, offering a framework for constructing stable dS vacua and inflationary scenarios within string theory. It also outlines future directions for CY$_3$ compactifications, multi-brane configurations, and warped backgrounds to extend these results.

Abstract

The KKLT construction of de Sitter vacua includes an uplifting term coming from an anti-D3-brane. Here we show how this term can arise via spontaneous breaking of supersymmetry, based on the emergence of a nilpotent chiral supermultiplet on the world-volume of the anti-D3-brane. We establish and use the fact that both the DBI as well as the WZ term, with account of orientifolding, acquire a form of the Volkov-Akulov action. For an O3 orientifold involution of $\mathbb{R}^{9,1}$ we demonstrate the cancellation between the fermionic parts of the DBI and WZ term for the D3-brane action. For the anti-D3-brane we show that the DBI action and the WZ action combine and lead to the emergence of the goldstino multiplet which is responsible for spontaneous breaking of supersymmetry. This provides a string theoretic explanation for the supersymmetric uplifting term in the KKLT effective supergravity model supplemented by a nilpotent chiral multiplet.

Emergence of Spontaneously Broken Supersymmetry on an Anti-D3-Brane in KKLT dS Vacua

TL;DR

The authors show that the KKLT uplifting term can be realized via spontaneous SUSY breaking on an anti-D3-brane, described by a nilpotent chiral multiplet with and a Volkov-Akulov goldstino. By imposing an O3 orientifold and a compatible κ-symmetry gauge, they demonstrate that the D3/anti-D3 world-volume actions reduce to Volkov-Akulov dynamics, yielding a 4D potential with the anti-D3 providing the goldstino multiplet. The anti-D3-brane contributes a doubled VA term, while the D3-brane can cancel under the same projection, establishing a concrete string-theoretic mechanism for SUSY breaking and uplift in KKLT. This work connects brane-worldvolume physics to manifestly supersymmetric 4D supergravity with nilpotent multiplets, offering a framework for constructing stable dS vacua and inflationary scenarios within string theory. It also outlines future directions for CY compactifications, multi-brane configurations, and warped backgrounds to extend these results.

Abstract

The KKLT construction of de Sitter vacua includes an uplifting term coming from an anti-D3-brane. Here we show how this term can arise via spontaneous breaking of supersymmetry, based on the emergence of a nilpotent chiral supermultiplet on the world-volume of the anti-D3-brane. We establish and use the fact that both the DBI as well as the WZ term, with account of orientifolding, acquire a form of the Volkov-Akulov action. For an O3 orientifold involution of we demonstrate the cancellation between the fermionic parts of the DBI and WZ term for the D3-brane action. For the anti-D3-brane we show that the DBI action and the WZ action combine and lead to the emergence of the goldstino multiplet which is responsible for spontaneous breaking of supersymmetry. This provides a string theoretic explanation for the supersymmetric uplifting term in the KKLT effective supergravity model supplemented by a nilpotent chiral multiplet.

Paper Structure

This paper contains 10 sections, 83 equations.

Table of Contents

  1. Introduction
  2. Classical actions for D3 and anti-D3 branes
  3. D3- and anti-D3-brane with orientifolding
  4. Compactification
  5. Discussion
  6. Appendix: D$p$-branes and anti-D$p$-branes with orientifolding
  7. $\theta^1=0$, $\theta^2=\lambda$, $X^{m^\prime}= \delta_\mu ^{m^\prime} \sigma^\mu$ gauge
  8. Supersymmetric truncation ${\cal F}=0, \,\Pi^I=0\, , (\mathbb{1}\pm q \Gamma)\theta=0$
  9. Evaluation of the action with ${\cal F}=0, \,\Pi^I=0\,, (\mathbb{1}+q \Gamma)\theta=0$ constraint
  10. Consistency of the supersymmetric truncation