Shape fluctuations of dual Dirac strings in the dual Higgs model with dual Dirac strings

The string shape fluctuations are integrated out in a dual Higgs model with dual Dirac strings. The effective string energy is calculated. By applying the ζ-function regularization it is shown that a Coulomb-like contribution has a standard form −αstringL, where L is a length of a string and αstring = π12 for opened strings. For closed strings one gets αstring = π3.