. . . To encourage the growth of any science, the best thing we can do is to meet together in its interest, to discuss its problems, to criticize each other's work and, best of all, to provide means by which the better portion of it may be made known to the world. . . .
The concept of topological phases and anomalies have been developed hand in hand; In the quantum Hall effect, if one focuses on the edge of the quantum Hall sample, the electromagnetic current is not conserved, as it "leaks" into the topological bulk, which is the origin of the quantized Hall conductance. The concept of topological phases in recent years has been expanded to include "symmetry-protected" topological phases such as the time-reversal symmetric topological insulators and the three-dimensional topological superconductors such as 3He B. In this talk, I will discuss gravitational responses of topological phases in terms of both infinitesimal and global gravitational anomalies.
In the first half of my talk, I will derive the thermal/mechanical analogue of the Streda formula. As the Streda formula of the electrical Hall conductivity, it links the quantum transport law to thermodynamics. When applied to the surface of the 3d topological superconductors, it predicts the thermal/mechanical analogue of the axion electrodynamics in the 3d topological insulators. In the second half of the talk, I will discuss how the *global* gravitational anomaly is useful to diagnose the stability of a symmetry-protected topological phase in two dimensions.