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• W3100872956 abstract "A bstract String theory provides us with 8d supersymmetric gauge theory with gauge algebras $$ mathfrak{s}mathfrak{u}(N),mathfrak{s}mathfrak{o}(2N),mathfrak{s}mathfrak{p}(N),{mathfrak{e}}_6,{mathfrak{e}}_7kern0.5em mathrm{and}kern0.5em {mathfrak{e}}_8 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>s</mml:mi> <mml:mi>u</mml:mi> <mml:mfenced> <mml:mi>N</mml:mi> </mml:mfenced> <mml:mo>,</mml:mo> <mml:mi>so</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>N</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> <mml:mi>p</mml:mi> <mml:mfenced> <mml:mi>N</mml:mi> </mml:mfenced> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>e</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>e</mml:mi> <mml:mn>7</mml:mn> </mml:msub> <mml:mspace /> <mml:mi>and</mml:mi> <mml:mspace /> <mml:msub> <mml:mi>e</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> , but no construction for $$ mathfrak{so}left(2N+1right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>so</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>N</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> , $$ {mathfrak{f}}_4 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>f</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> and $$ {mathfrak{g}}_2 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>g</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> is known. In this paper, we show that the theories for $$ {mathfrak{f}}_4 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>f</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> and $$ mathfrak{so}left(2N+1right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>so</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>N</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> have a global gauge anomaly associated to π d =8 , while $$ {mathfrak{g}}_2 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>g</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> does not have it. We argue that the anomaly associated to π d in d -dimensional gauge theories cannot be canceled by topological degrees of freedom in general. We also show that the theories for $$ mathfrak{s}mathfrak{p}(N) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>s</mml:mi> <mml:mi>p</mml:mi> <mml:mfenced> <mml:mi>N</mml:mi> </mml:mfenced> </mml:math> have a subtler gauge anomaly, which we suggest should be canceled by a topological analogue of the Green-Schwarz mechanism." @default.
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• W3100872956 date "2017-11-01" @default.
• W3100872956 modified "2023-10-18" @default.
• W3100872956 title "8d gauge anomalies and the topological Green-Schwarz mechanism" @default.
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• W3100872956 doi "https://doi.org/10.1007/jhep11(2017)177" @default.
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