The twisted/untwisted representation category of the Heisenberg conformal net is the continuous Tambara-Yamagami category TY(R, chi_-, +1), whose Z/2-equivariantization describes representations of the fixed-point net.
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The crossed braided tensor category of twisted and untwisted representations of the Heisenberg conformal net
The twisted/untwisted representation category of the Heisenberg conformal net is the continuous Tambara-Yamagami category TY(R, chi_-, +1), whose Z/2-equivariantization describes representations of the fixed-point net.