PIRSA:13020148

Gravitational anomaly and topological phases

Ryu, S. (2013). Gravitational anomaly and topological phases. Perimeter Institute. https://pirsa.org/13020148

Ryu, Shinsei. Gravitational anomaly and topological phases. Perimeter Institute, Feb. 28, 2013, https://pirsa.org/13020148 

          @misc{ pirsa_PIRSA:13020148,
            doi = {10.48660/13020148},
            url = {https://pirsa.org/13020148},
            author = {Ryu, Shinsei},
            keywords = {Condensed Matter},
            language = {en},
            title = {Gravitational anomaly and topological phases},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {feb},
            note = {PIRSA:13020148 see, \url{https://pirsa.org}}
          }

Shinsei Ryu University of Illinois at Urbana-Champaign (UIUC)

DOI 10.48660/13020148
Collection
Talk Type Scientific Series
Subject

Abstract

Since the quantum Hall effect, the notion of topological phases of matter has been extended to those that are well-defined (or: ``protected'') in the presence of a certain set of symmetries, and that exist in dimensions higher than two. In the (fractional) quantum Hall effects (and in ``chiral'' topological phases in general), Laughlin's thought experiment provides a key insight into their topological characterization; it shows a close connection between topological phases and quantum anomalies. By taking various examples, I will demonstrate that quantum anomalies serve as a useful tool to diagnose (and even define) topological properties of the systems. For chiral topological phases in (2+1) dimensions and (3+1) dimensional topological superconductors, I will discuss topological responses of the system which involve a cross correlation between thermal transport, angular momentum, and entropy. We also argue that gravitational anomaly is useful to study symmetry protected topological phases in (2+1) dimensions.