Holographic QFTs on S2×S2, spontaneous symmetry breaking and Efimov saddle points

Holographic CFTs and holographic RG flows on space-time manifolds which are d-dimensional products of spheres are investigated. On the gravity side, this corresponds to Einstein-dilaton gravity on an asymptotically AdSd+1 geometry, foliated by a product of spheres. We focus on holographic theories on S2× S2, we show that the only regular five-dimensional bulk geometries have an IR endpoint where one of the sphere shrinks to zero size, while the other remains finite. In the Z2-symmetric limit, where the two spheres have the same UV radii, we show the existence of a infinite discrete set of regular solutions, satisfying an Efimov-like discrete scaling. The Z2-symmetric solution in which both spheres shrink to zero at the endpoint is singular, whereas the solution with lowest free energy is regular and breaks Z2 symmetry spontaneously. We explain this phenomenon analytically by identifying an unstable mode in the bulk around the would-be Z2-symmetric solution. The space of theories have two branches that are connected by a conifold transition in the bulk, which is regular and correspond to a quantum first order transition. Our results also imply that AdS5 does not admit a regular slicing by S2× S2.

Multi-scale Simulation in Railway Planning and Operation

Simulation methods are widely used in railway planning and operation. However, at the moment there are no applicable solutions in the process simulation for a smooth transition among different infrastructure levels on the basis of a unified structure with consistent algorithm. In this paper, a multi-scale simulation model is designed with consideration of the level of detail of the investigated infrastructure model and the homogeneity of the processes running in the simulation model. A comprehensive and synthesized view of railway planning and operation is therefore obtained. Within the multi-scale simulation model, railway planning and operation processes can be simulated, evaluated and optimized consistently. KEY WORDS: railway planning, simulation, multi-scale, aggregation, discrete scaling, continuous scaling, homogenous process, inhomogeneous process