Particle theory

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.

Abstract:

We consider the model of hard dimers coupled to two-dimensional causal dynamical triangulations (CDT) with all dimer types present and solve it exactly subject to a single restriction. Depending on the dimer weights there are, in addition to the usual gravity phase of CDT, two tri-critical and two dense dimer phases. We establish the properties of these phases, computing their cylinder and disk amplitudes, and their scaling limits.