2024/12/30 by Zheyan Wan, Juven Wang, Wan, Zheyan +3 · 1 citation
Computer Science · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2412.21196
openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The local Lie algebra of the Standard Model (SM) is su(3)× su(2) × u(1), yet its global gauge group, G_\rm SM\rm q=SU(3)×SU(2)×U(1)/ℤ\rm q, q=1,2,3,6 remains undetermined. Building on previous work on 4d anomalies and 5d cobordism invariants, we classify lower-dimensional invertible field theories (iFTs) or symmetry-protected topological states (SPTs) in 4d, 3d, 2d, and 1d. While the integer SPTs are hard to detect, the fractional SPTs produce measurable topological responses. In particular, the symmetry fractionalization labeled by k∈ℤ_6/\rm q in [arXiv:2411.18160] introduces the symmetry-enriched SM variants, denoted as SM_(\rm q,k). We further introduce a new integer n series of baryon-minus-lepton (\bf B-\bf L)-like U(1) symmetries, Xn ≡ n (B-L) + (1-(n)/(Nc))Y with electroweak hypercharge Y, n≥1, Nc=3, where the charge qXn = q_Y \mod n. Analyzing the symmetry-enriched SM with 0-form and 1-form symmetries (G[0], G[1]), symmetry-twist group homomorphism ρ, and symmetry frationalization obstruction [β], their spacetime-internal gauge bundle constraints, and their mixed anomalies, we derive the fractional topological response σn(\rm q,k)=\frac\rm q(1-n)gcd(2,n)2n+\frack\rm q6\mod1. Our σn response requires more general Spinc manifolds for odd n and Spin manifolds for even n. For a given n (with n≥ 7 and n≠ 10,12,15,30), σn uniquely fixes the gauge group parameter q and fractionalization label k. Moreover, using pairs such as (n1,n2)=(2,3),(2,5),(3,4),(3,5),(4,5), etc. uniquely distinguishes SM_(\rm q,k). Our results illuminate the global structure of the SM gauge group via measurable topological responses.