Properties of the new $$ \mathcal{N} $$ = 1 AdS4 vacuum of maximal supergravity
Nikolay Bobev, Thomas Fischbacher, Krzysztof Pilch
Abstract
A bstract The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 8, SO(8) gauged supergravity using Machine Learning software in [1] has led to a discovery of a new $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3) × ℤ 2 -invariant truncation of the $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 8 theory to an $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3) × ℤ 2 -invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional $$ {\mathbb{Z}}_2^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ℤ</mml:mi> <mml:mn>2</mml:mn> <mml:mn>3</mml:mn> </mml:msubsup> </mml:math> -invariant scalar manifold (SU(1 , 1) / U(1)) 7 , for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7 , 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 AdS 4 solution and the maximally supersymmetric AdS 4 vacuum. Using holography, this result indicates the existence of an $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.