Weyl Invariance and Spurious Black Hole in Two-Dimensional Dilaton Gravity

In two-dimensional dilaton gravity theories, there may exist a global Weyl invariance which makes black hole spurious. If the global invariance and the local Weyl invariance of the matter coupling are intact at the quantum level, there is no Hawking radiation. We explicitly verify the absence of anomalies in these symmetries for the model proposed by Callan, Giddings, Harvey and Strominger. The crucial observation is that the conformal anomaly can be cohomologically trivial and so not truly anomalous in such dilaton gravity models.Comment: 28 pages, KANAZAWA-93-0

Super-Virasoro Anomaly, Super-Weyl Anomaly and the Super-Liouville Action for 2D Supergravity

The relation between super-Virasoro anomaly and super-Weyl anomaly in $N=1$ NSR superstring coupled with 2D supergravity is investigated from canonical theoretical view point. The WZW action canceling the super-Virasoro anomaly is explicitly constructed. It is super-Weyl invariant but nonlocal functional of 2D supergravity. The nonlocality can be remedied by the super-Liouvlle action, which in turn recovers the super-Weyl anomaly. The final gravitational effective action turns out to be local but noncovariant super-Liouville action, describing the dynamical behavior of the super-Liouville fields. The BRST invariance of this approach is examined in the superconformal gauge and in the light-cone gauge.Comment: 45 page

Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions

We study a Majorana zero-energy state bound to a hedgehog-like point defect in a topological superconductor described by a Bogoliubov-de Gennes (BdG)-Dirac type effective Hamiltonian. We first give an explicit wave function of a Majorana state by solving the BdG equation directly, from which an analytical index can be obtained. Next, by calculating the corresponding topological index, we show a precise equivalence between both indices to confirm the index theorem. Finally, we apply this observation to reexamine the role of another topological invariant, i.e., the Chern number associated with the Berry curvature proposed in the study of protected zero modes along the lines of topological classification of insulators and superconductors. We show that the Chern number is equivalent to the topological index, implying that it indeed reflects the number of zero-energy states. Our theoretical model belongs to the BDI class from the viewpoint of symmetry, whereas the spatial dimension of the system is left arbitrary throughout the paper.Comment: 12 page

Contrastive Multiple Correspondence Analysis (cMCA): Using Contrastive Learning to Identify Latent Subgroups in Political Parties

Scaling methods have long been utilized to simplify and cluster high-dimensional data. However, the latent spaces derived from these methods are sometimes uninformative or unable to identify significant differences in the data. To tackle this common issue, we adopt an emerging analysis approach called contrastive learning. We contribute to this emerging field by extending its ideas to multiple correspondence analysis (MCA) in order to enable an analysis of data often encountered by social scientists -- namely binary, ordinal, and nominal variables. We demonstrate the utility of contrastive MCA (cMCA) by analyzing three different surveys of voters in Europe, Japan, and the United States. Our results suggest that, first, cMCA can identify substantively important dimensions and divisions among (sub)groups that are overlooked by traditional methods; second, for certain cases, cMCA can still derive latent traits that generalize across and apply to multiple groups in the dataset; finally, when data is high-dimensional and unstructured, cMCA provides objective heuristics, above and beyond the standard results, enabling more complex subgroup analysis.Comment: Both authors contributed equally to the paper and listed alphabetically. This manuscript is currently under revie