Systematic exploration of the non-geometric flux landscape

Abstract Given the huge size of the generic four-dimens-ional scalar potentials arising from the type II supergravities based on toroidal orientifolds, it is even hard to analytically solve the extremization conditions, and therefore the previous studies have been mainly focused on taking some numerical approaches. In this work, using the so-called axionic flux polynomials we demonstrate that the scalar potential and the extremization conditions can be simplified to a great extent, leading to the possibility of performing an analytic exploration of the flux landscape. In this regard, we consider the isotropic case of a type IIB model based on the standard $${\mathbb T}^6/({\mathbb Z}_2 \times {\mathbb Z}_2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mn>6</mml:mn> </mml:msup> <mml:mo>/</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>×</mml:mo> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> orientifold having the three-form fluxes $$F_3/H_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> and the non-geometric Q -flux. This model results in around 300 terms in the scalar potential which depend on 6 moduli/axionic fields and 14 flux parameters. Considering that the axionic flux polynomials can take either zero or non-zero values results in the need of analyzing $$2^{14}=16{,}384$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>14</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>16</mml:mn> <mml:mo>,</mml:mo> <mml:mn>384</mml:mn> </mml:mrow> </mml:math> candidate configurations, and we find that more than 16,200 of those result in No-Go scenarios for Minkowskian/de-Sitter vacua. Based on our systematic exploration of non-tachyonic flux vacua, we present a detailed classification of such No-Go scenarios as well as the leftover “undecided” configurations for which we could not conclude about the presence/absence of the stable Minkowskian/de-Sitter vacua.