The notion that the geometry of spacetime is given by the moduli space of 0-branes is examined in four examples of Calabi-Yau threefolds. An important consideration when determining the moduli space of D-branes is the stability condition and this is key in our analysis. In the first two examples, the flop and the orbifold blowup, no surprises are found. Next, an exoflop is considered where the linear sigma model implies a CP1 external to the Calabi-Yau threefold is part of the geometry. The 0-brane probe sees no such external CP1 and furthermore exhibits a surprising discontinuity when following an extremal transition associated to the exoflop. Finally we consider a hybrid model of a Landau--Ginzburg fibration over a CP1. Using the technology of matrix factorizations we find a D-brane probe whose moduli space is this CP1 but it is not a 0-brane and is not stable at the large radius limit of the Calabi-Yau manifold.
Probing the Singularity of Scalar-Haired Black Holes with Holographic Complexity
Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎大学）；Departement Physik, ETH Zürich（苏黎世联邦理工学院物理系）；Département de Physique, École Polytechnique, IP Paris（巴黎综合理工学院物理系）
Probing Probability Geometry with Schwinger--Dyson Identities: Score Mismatch, Fisher Information, and Configurational Temperature
National Institute for Theoretical and Computational Sciences, School of Physics, and Mandelstam Institute for Theoretical Physics, University of the Witwatersrand（威特沃特斯兰德大学理论计算科学国家研究所、物理学院及曼德尔斯坦理论物理研究所）；Brown Center for Theoretical Physics and Innovation, Department of Physics, Brown University（布朗大学物理系理论物理与创新中心）
