TY - JOUR
T1 - On arithmetic Dijkgraaf-Witten theory
AU - Hirano, Hikaru
AU - Kim, Junhyeong
AU - Morishita, Masanori
N1 - Publisher Copyright:
© 2023, Communications in Number Theory and Physics.All Rights Reserved.
PY - 2023
Y1 - 2023
N2 - We present basic constructions and properties in arithmetic Chern-Simons theory with finite gauge group along the line of topological quantum field theory. For a finite set S of finite primes of a number field k, we construct arithmetic analogues of the Chern-Simons 1-cocycle, the prequantization bundle for a surface and the Chern-Simons functional for a 3-manifold.We then construct arithmetic analogues for k and S of the quantum Hilbert space (space of conformal blocks) and the Dijkgraaf-Witten partition function in (2+1)-dimensional Chern-Simons TQFT. We show some basic and functorial properties of those arithmetic analogues.
AB - We present basic constructions and properties in arithmetic Chern-Simons theory with finite gauge group along the line of topological quantum field theory. For a finite set S of finite primes of a number field k, we construct arithmetic analogues of the Chern-Simons 1-cocycle, the prequantization bundle for a surface and the Chern-Simons functional for a 3-manifold.We then construct arithmetic analogues for k and S of the quantum Hilbert space (space of conformal blocks) and the Dijkgraaf-Witten partition function in (2+1)-dimensional Chern-Simons TQFT. We show some basic and functorial properties of those arithmetic analogues.
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U2 - 10.4310/CNTP.2023.v17.n1.a1
DO - 10.4310/CNTP.2023.v17.n1.a1
M3 - Article
AN - SCOPUS:85152040032
SN - 1931-4523
VL - 17
SP - 1
EP - 61
JO - Communications in Number Theory and Physics
JF - Communications in Number Theory and Physics
IS - 1
ER -