Warped $$\hbox {G}_2$$-throats in IIA and uplift dSillusions

Abstract Flux compactifications of IIA supergravity on orientifolded $$\hbox {G}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>G</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -manifolds have been argued to allow for classical $$\hbox {Minkowski}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Minkowski</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:math> vacua with moduli and scale-separated $$\hbox {AdS}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>AdS</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:math> vacua with full moduli stabilisation. To further uplift these vacua to meta-stable $$\hbox {dS}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>dS</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:math> vacua using anti-D2 branes, warped throats are desirable. We study the flux-stabilisation of local “CGLP-type” throats in compact $$\hbox {G}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>G</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> spaces, and discuss consistency constraints on anti-brane uplifting. Despite the classical $$\hbox {AdS}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>AdS</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:math> vacua being free of tachyons, we find that uplifting from anti-branes down warped throats is forbidden. If instead we rely on hypothetical $$\hbox {AdS}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>AdS</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:math> vacua that arise from quantum corrections to the classical $$\hbox {Minkowski}_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Minkowski</mml:mtext> <mml:mn>3</mml:mn> </mml:msub> </mml:math> vacua, we find that (similarly to the 4d analogues) consistency constraints point in opposite directions. However, there is potentially an advantage over 4d when it comes to concrete fine-tuning freedom of numbers, such as tadpole constraints.