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$\overline{\rm D3}$ and dS

Eric A. Bergshoeff, Keshav Dasgupta, Renata Kallosh, Antoine Van Proeyen, Timm Wrase

TL;DR

This work demonstrates that the uplifting role of the $\overline{\rm D3}$ brane in KKLT remains consistent when worldvolume fermions are included in a GKP background preserving $\mathcal{N}=1$ in four dimensions. The analysis shows that ISD flux with $(2,1)$ components removes the $SU(3)$ fermion triplet while leaving a massless SU(3) singlet goldstino, enabling a Volkov-Akulov-type realization of spontaneously broken $\mathcal{N}=1$ supersymmetry in the low-energy theory. The authors derive the quadratic-in-fermions actions for the D3 and $\overline{\rm D3}$ branes in curved space, establish the cancellation/doubling pattern in this background, and connect the resulting effective theory to a 4d supergravity with a nilpotent multiplet $S$ and a de Sitter uplift. They further illustrate how the uplifting contribution can be incorporated in KKLT-like constructions with either standard or highly warped Kähler potentials, and discuss no-go conditions and their circumvention via quantum corrections. Overall, the paper provides a string-theoretic, fermion-level justification for de Sitter vacua with spontaneously broken SUSY in KKLT, via a nilpotent goldstino sector arising from the $\overline{\rm D3}$ brane on O3 planes in GKP backgrounds.

Abstract

The role of the $\overline{\rm D3}$ brane in providing de Sitter vacua with spontaneously broken supersymmetry in the KKLT construction is clarified. The first step in this direction was explained in arXiv:hep-th/0301240, arXiv:hep-th/0308055: it was shown there that in the GKP background the bosonic contributions to the vacuum energy from the DBI and WZ term cancel for a D3 brane, but double for a $\overline{\rm D3}$ brane, leading to de Sitter vacua. The next step was taken in arXiv:1411.1121 where the analogous mechanism of the doubling (cancelation) of the $\overline{\rm D3}$ (D3) DBI and WZ terms was discovered in the presence of Volkov-Akulov fermions living on the brane, in a flat supergravity background. Here we confirm this mechanism of doubling/cancelation for the $\overline{\rm D3}$/D3 brane in the GKP supergravity background preserving $\mathcal{N}=1$, $d=4$ supersymmetry. We find that imaginary self-dual $G_{(3)}$ flux of type $(2,1)$ nicely removes the $SU(3)$ fermion triplet by giving it a large mass, while leaving the Volkov-Akulov goldstino, which is the $SU(3)$ singlet, massless. This makes the de Sitter landscape in D-brane physics clearly related to de Sitter vacua in effective $d=4$ supergravity with a nilpotent multiplet and spontaneously broken supersymmetry.

$\overline{\rm D3}$ and dS

TL;DR

This work demonstrates that the uplifting role of the brane in KKLT remains consistent when worldvolume fermions are included in a GKP background preserving in four dimensions. The analysis shows that ISD flux with components removes the fermion triplet while leaving a massless SU(3) singlet goldstino, enabling a Volkov-Akulov-type realization of spontaneously broken supersymmetry in the low-energy theory. The authors derive the quadratic-in-fermions actions for the D3 and branes in curved space, establish the cancellation/doubling pattern in this background, and connect the resulting effective theory to a 4d supergravity with a nilpotent multiplet and a de Sitter uplift. They further illustrate how the uplifting contribution can be incorporated in KKLT-like constructions with either standard or highly warped Kähler potentials, and discuss no-go conditions and their circumvention via quantum corrections. Overall, the paper provides a string-theoretic, fermion-level justification for de Sitter vacua with spontaneously broken SUSY in KKLT, via a nilpotent goldstino sector arising from the brane on O3 planes in GKP backgrounds.

Abstract

The role of the brane in providing de Sitter vacua with spontaneously broken supersymmetry in the KKLT construction is clarified. The first step in this direction was explained in arXiv:hep-th/0301240, arXiv:hep-th/0308055: it was shown there that in the GKP background the bosonic contributions to the vacuum energy from the DBI and WZ term cancel for a D3 brane, but double for a brane, leading to de Sitter vacua. The next step was taken in arXiv:1411.1121 where the analogous mechanism of the doubling (cancelation) of the (D3) DBI and WZ terms was discovered in the presence of Volkov-Akulov fermions living on the brane, in a flat supergravity background. Here we confirm this mechanism of doubling/cancelation for the /D3 brane in the GKP supergravity background preserving , supersymmetry. We find that imaginary self-dual flux of type nicely removes the fermion triplet by giving it a large mass, while leaving the Volkov-Akulov goldstino, which is the singlet, massless. This makes the de Sitter landscape in D-brane physics clearly related to de Sitter vacua in effective supergravity with a nilpotent multiplet and spontaneously broken supersymmetry.

Paper Structure

This paper contains 12 sections, 82 equations.

Table of Contents

  1. Introduction
  2. The D3 and Bar D3 brane actions in curved superspace
  3. A short review of Volkov-Akulov supersymmetry
  4. Kappa-invariant worldvolume actions
  5. Bar D3 and D3 in a flat superspace background, with orientifolding
  6. Bar D3 and D3 in a curved superspace background with unbroken N=1 supersymmetry
  7. The D3 brane and bar D3 brane actions quadratic in fermions
  8. The bar D3 brane action in a GKP background
  9. Discussion
  10. Spinor reduction from d=10 to d=4
  11. A toroidal example
  12. A note on the no-go theorem for dS space