2025/08/07 by Orii, Ippo · 1 citation
#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.2508.04990
We study time-reversal symmetry in (2+1)-dimensional abelian bosonic topological phases. Z2 x Z2 classifies the time-reversal anomalies in such systems symmetry-protected topological (SPT) phases in (3+1) dimensions and can be diagnosed via partition functions on manifolds such as RP4 and CP2. These partition functions are related by an anomaly formula of the form Z(RP4) * Z(CP2) = thetaM, where thetaM is the Dehn twist phase associated with the crosscap state. Meanwhile, the existence of gapped boundaries is constrained by so-called higher central charges, denoted xin, which serve as computable invariants encoding obstruction data. Motivated by the known relation Z(CP2) = xi1, we propose a generalization of the anomaly formula involving both the higher central charges xin and a new time-reversal invariant etan. By introducing a distinguished subset Mn of the set A of anyons, we establish the relation etan * xin = (sum of theta(a)n over a in Mn) divided by its absolute value. This generalizes the known anomaly formula. We analyze the algebraic structure of the subset Mn, derive consistency relations it satisfies, and clarify its connection to the original anomaly formula.