Speaker
Description
A topological quantum field theory (TQFT) is a class of field theories that have been successfully formulated in a mathematically rigorous way, providing a framework for describing physical phenomena independent of the spacetime metric. In particular, (2+1)-dimensional TQFTs—exemplified by Chern–Simons theory—have been extensively studied in both high-energy and condensed-matter physics as toy models of low-dimensional quantum gravity and as effective theories describing the fractional quantum Hall effect.
TQFTs with time-reversal symmetry are equivalent to considering such theories on non-orientable manifolds. However, While these systems exhibit rich mathematical structures, many physical aspects remain unresolved, and a complete mathematical formulation is still lacking. Among the most important objects for analyzing time-reversal-symmetric TQFTs is the crosscap state, which captures the essential features of non-orientable TQFTs.
In this talk, I will introduce the axioms of a TQFT, then provide an overview of the current understanding of systems with time-reversal symmetry through the study of crosscap states, incorporating some of my recent results. If time permits, I will also present a new idea suggesting that the study of crosscap states may contain key insights toward a rigorous mathematical formulation of non-orientable TQFTs.
