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• W1529168148 abstract "In this paper, we systematically study gauge anomalies in bosonic and fermionic weak-coupling gauge theories with gauge group G (which can be continuous or discrete). We show a very close relation between gauge anomalies and symmetry-protected trivial (SPT) orders [also known as symmetry-protected topological (SPT) orders] in one-higher dimensions. Using such an idea, we argue that, in d space-time dimensions, the gauge anomalies are described by the elements in Free[H^{d+1}(G,R/Z)]oplus H_pi^{d+1}(BG,R/Z). The well known Adler-Bell-Jackiw anomalies are classified by the free part of the group cohomology class H^{d+1}(G,R/Z) of the gauge group G (denoted as Free[H^{d+1}(G,R/Z)]). We refer other kinds of gauge anomalies beyond Adler-Bell-Jackiw anomalies as nonABJ gauge anomalies, which include Witten SU(2) global gauge anomaly. We introduce a notion of pi-cohomology group, H_pi^{d+1}(BG,R/Z), for the classifying space BG, which is an Abelian group and include Tor[H^{d+1}(G,R/Z)] and topological cohomology group H^{d+1}(BG,R/Z) as subgroups. We argue that H_pi^{d+1}(BG,R/Z) classifies the bosonic nonABJ gauge anomalies, and partially classifies fermionic nonABJ anomalies. Using the same approach that shows gauge anomalies to be connected to SPT phases, we can also show that gravitational anomalies are connected to topological orders (ie patterns of long-range entanglement) in one-higher dimension." @default.
• W1529168148 created "2016-06-24" @default.
• W1529168148 creator A5072166156 @default.
• W1529168148 date "2013-08-09" @default.
• W1529168148 modified "2023-10-05" @default.
• W1529168148 title "Classifying gauge anomalies through symmetry-protected trivial orders and classifying gravitational anomalies through topological orders" @default.
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• W1529168148 doi "https://doi.org/10.1103/physrevd.88.045013" @default.
• W1529168148 hasPublicationYear "2013" @default.
• W1529168148 type Work @default.
• W1529168148 sameAs 1529168148 @default.

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