Study of gapped phases of 4d gauge theories using temporal gauging of the ℤN 1-form symmetry

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As exactly N 2 of the ZtH [˜

e′ , e 3 ; m

˜ ′ , m3 ] equal 1 while all the others vanish, this equality

can be true iff exp 2πi

e·m

˜′ −m

˜ · e˜′ ) = 1 for each light flux (˜

e′ , e 3 ; m

˜ ′ , m3 ). □

N (˜

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