Challenge for spontaneous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:math> violation in Type IIB orientifolds with fluxes

Abstract

We systematically investigate the possibilities of realizing the spontaneous $CP$ violation in Type IIB flux compactifications on toroidal orientifolds. Our detailed analysis for a generic choice of three-form fluxes leads to the presence of flat directions, where $CP$-breaking and -conserving vacua are degenerate, indicating that flux compactifications are not sufficient to realize the spontaneous $CP$ violation. Furthermore, the four-dimensional $CP$ can be embedded into the duality symmetries, namely modular symmetries for a particular choice of fluxes.

Topics & Concepts