On dimensions of (2+1)D abelian bosonic topological systems on unoriented manifolds

2025/02/19 by Orii, Ippo · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2502.13532

Abstract

We give a framework to describe abelian bosonic topological systems with parity symmetry on a torus in terms of the representation of GL(2,\bZ). However, this information alone does not guarantee that we can assign Hilbert spaces to unoriented surfaces in a way compatible with the gluing axiom of topological quantum field theory. Here, we show that we can assign Hilbert spaces with integer dimensions to unoriented surfaces in the case of abelian bosonic topological systems with time-reversal symmetry.

Cited by

• Entanglement Spectrum Resolved by Loop Symmetries
• Vanishing of the H³ obstruction for time-reversal symmetry in (2+1)D abelian bosonic TQFTs
• Generalization of anomaly formula for time reversal symmetry in (2+1)D abelian bosonic TQFTs
• Web of dualities on non-orientable surfaces

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