A 10d view on the KKLT AdS vacuum and uplifting
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Springer
Received: February Revised: March Accepted: May Published: June
25, 20, 24, 10,
2019 2020 2020 2020
F.F. Gautason, V. Van Hemelryck, T. Van Riet and G. Venken Institute of Theoretical Physics, KU Leuven, Celestijnenlaan 200D B-3001 Leuven, Belgium
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We analyse the ten-dimensional Einstein equations in the KKLT setting. We verify that the quartic gaugino term is needed to remove singularities in the on-shell action as suggested by Hamada et al. We contrast two approaches that have been taken in the literature when employing the effect of gaugino condensation in the ten-dimensional equations of motion. Here we follow the proposal to insert explicit non-zero fermion bilinar vev into the localised energy-momentum tensor of the 7-branes obtained from varying the 10d off-shell action with respect to the 10d metric. Our procedure is common in semi-classical physics and is manifestly local in 10d. However, it does not lead to the KKLT effective field theory. The alternative procedure of deriving the energy momentum tensor after replacing fermion bilinears by the gaugino vev, might be less well motivated in 10d, but reproduces the results of the KKLT effective field theory. Keywords: D-branes, Flux compactifications, Superstring Vacua ArXiv ePrint: 1902.01415
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)074
JHEP06(2020)074
A 10d view on the KKLT AdS vacuum and uplifting
Contents 1
2 The framework
3
3 A subtlety in the semi-classical Einstein equations
4
4 The four-dimensional cosmological constant
5
5 Comparing to KKLT
9
6 Discussion 6.1 Summary and discussion of results 6.2 Comparison with recent papers
11 11 12
A Conventions
14
B Variation of the action
14
C (Non)renormalisation of the Chern-Simons action
16
1
Introduction
Moduli stabilisation in string theory has a long history and its understanding is crucial for the study of top-down phenomenology. One of the main breakthroughs came in 2003 with the KKLT model [1] and in 2005 with the Large Volume Scenario [2]. Both methods to stabilise moduli rely on computing leading-order corrections to ten-dimensional supergravity solutions with orientifold sources and three-form fluxes in type IIB supergravity [3–5]. Despite the long history of this field there has never been any genuine top-down understanding of these mechanisms to stabilise moduli. The arguments always involved a mixture between top-down and bottom-up viewpoints. This is not a problem per se, but it can lead to a false sense of freedom to tune parameters in the bottom-up effective field theory. It is therefore desirable to find at least one concrete top-down description of moduli-stabilisation. Recently the field of moduli stabilisation has regained attention due to a growing suspicion that string theory may fail to accommodate any de Sitter (dS) vacuum [6–8]. This suspicion is mainly based on three things. Fi
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