Bubble instabilities of mIIA on AdS$_4\times S^6$
Pieter Bomans, Davide Cassani, Giuseppe Dibitetto, Nicolò Petri
Abstract
We consider compactifications of massive IIA supergravity on a six-sphere. This setup is known to give rise to non-supersymmetric AdS _4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>4</mml:mn> </mml:msub> </mml:math> vacua preserving \mathrm{SO}(7) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mstyle mathvariant="normal"> <mml:mi>S</mml:mi> <mml:mi>O</mml:mi> </mml:mstyle> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>7</mml:mn> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> as well as G _2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> residual symmetry. Both solutions have a round S^6 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>6</mml:mn> </mml:msup> </mml:math> metric and are supported by the Romans’ mass and internal F_{6} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>6</mml:mn> </mml:msub> </mml:math> flux. While the \mathrm{SO}(7) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mstyle mathvariant="normal"> <mml:mi>S</mml:mi> <mml:mi>O</mml:mi> </mml:mstyle> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>7</mml:mn> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> invariant vacuum is known to be perturbatively unstable, the G _2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> invariant one has been found to have a fully stable Kaluza-Klein spectrum. Moreover, it has been shown to be protected against brane-jet instabilities. Motivated by these results, we study possible bubbling solutions connected to the G _2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> vacuum, representing non-perturbative instabilities of the latter. We indeed find an instability channel represented by the nucleation of a bubble of nothing dressed up with a homogeneous D2 brane charge distribution in the internal space. Our solution generalizes to the case where S^6 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>6</mml:mn> </mml:msup> </mml:math> is replaced by any six-dimensional nearly-K"ahler manifold.