Abstract
We present a detailed study of the effective cones of Calabi-Yau threefolds with h1,1 = 2, including the possible types of walls bounding the Kähler cone and a classification of the intersection forms arising in the geometrical phases. For all three normal forms in the classification we explicitly solve the geodesic equation and use this to study the evolution near Kähler cone walls and across flop transitions in the context of M-theory compactifications. In the case where the geometric regime ends at a wall beyond which the effective cone continues, the geodesics “crash” into the wall, signaling a breakdown of the M-theory supergravity approximation. For illustration, we characterise the structure of the extended Kähler and effective cones of all h1,1 = 2 threefolds from the CICY and Kreuzer-Skarke lists, providing a rich set of examples for studying topology change in string theory. These examples show that all three cases of intersection form are realised and suggest that isomorphic flops and infinite flop sequences are common phenomena.
Highlights
Topology change is an intriguing feature of string theory, and possibly of quantum gravity more generally, which was first discovered and studied some time ago [1–7]
We present a detailed study of the effective cones of Calabi-Yau threefolds with h1,1 = 2, including the possible types of walls bounding the Kähler cone and a classification of the intersection forms arising in the geometrical phases
We review the different types of Kähler cone walls, namely flop walls, walls along which a divisor collapses to a curve or a point, and effective cone walls on which the volume of the CY goes to zero, and show how they can be identified from basic topological CY data, as well as discuss the properties of the moduli space metric near these walls
Summary
Topology change is an intriguing feature of string theory, and possibly of quantum gravity more generally, which was first discovered and studied some time ago [1–7]. To substantiate our discussion we have compiled a detailed dataset which contains the cone and wall structure of the extended and effective cones for all h1,1(X) = 2 manifolds within the complete intersection CYs (CICYs) [12] and the CY hypersurfaces in toric fourfolds (THCYs) [13]. This data shows that the Kähler moduli space structure is quite rich, even at the level of Picard number two, and it should provide a useful resource for future studies of topology change in string theory.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
