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Theta terms and asymptotic behavior of gauge potentials in (3+1) dimensions
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We describe paths in the configuration space of (3+1) dimensional QED whose relative quantum phase (or relative phase in the functional integral) depends on the value of the theta angle. The final configurations on the two paths are related by a gauge transformation but differ in magnetic helicity or Chern-Simons number. Such configurations must exhibit gauge potentials that fall off no faster than 1/r in some region of finite solid angle, although they need not have net magnetic charge (i.e., are not magnetic monopoles). The relative phase is proportional to theta times the difference in Chern-Simons number. We briefly discuss some possible implications for QCD and the strong CP problem.
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The Line operators in the G2HDM model
The true gauge group of the G2HDM can differ by a discrete center quotient, and this choice changes the allowed line operators, theta-angle periodicities, and minimal electric and magnetic charges after symmetry breaking.
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