A cornucopia of AdS5 vacua

Abstract

A bstract We report on a systematic search for AdS 5 vacua corresponding to critical points of the potential in the five-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 8 SO(6) gauged supergravity. By employing Google’s TensorFlow Machine Learning library, we find the total of 32 critical points including 5 previously known ones. All 27 new critical points are non-supersymmetric. We compute the mass spectra of scalar fluctuatons for all points and find that the non- supersymmetric AdS 5 vacua are perturbatively unstable. Many of the new critical points can be found analytically within consistent truncations of the $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 8 supergravity with respect to discrete subgroups of the S(O(6) × GL(2 , ℝ)) symmetry of the potential. In par- ticular, we discuss in detail a $$ {\mathrm{\mathbb{Z}}}_2^3 $$ <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 truncation with 10 scalar fields and 15 critical points. We also compute explicitly the scalar potential in a $$ {\mathrm{\mathbb{Z}}}_2^2 $$ <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>2</mml:mn> </mml:msubsup> </mml:math> -invariant extension of that truncation to 18 scalar fields and reproduce 17 of the 32 critical points from the numerical search. Finally, we show that the full potential as a function of 42 scalar fields can be studied analytically using the so-called solvable parametrization. In particular, we find that all critical points lie in a ℤ 2 -invariant subspace spanned by 22 scalar fields.

Topics & Concepts