Modular Anomalies in (2+1) and (3+1)-D Edge Theories

Understand

The classification of topological phases of matter in the presence of interactions is an area of intense interest.

• One possible means of classification is via studying the partition function under modular transforms, as the presence of an anomalous phase arising in the edge theory of a D-dimensional system under modular transformation, or modular anomaly, signals the presence of a (D+1)-D non-trivial bulk.
• In this work, we discuss the modular transformations of conformal field theories along a (2+1)-D and a (3+1)-D edge.
• Using both analytical and numerical methods, we show that chiral complex free fermions in (2+1)-D and (3+1)-D are modular invariant.