Strings in the Abelian Higgs model and QCD

We review recent progress in string representations of the Abelian Higgs Model and gluodynamics. In the first case, the partition function could be cast into the form of a sum over string world-sheets, while in the second case the string effective action follows from the Wilson loop expansion by making use of the Method of Vacuum Correlators. This enables one to express the string tension of the Nambu-Goto term and the rigidity term coupling constant via the gauge-invariant correlator of two gluonic field strength tensors, known from the lattice data. According to these data, the rigidity term coupling constant is obtained to be negative, which means the stability of strings. The Hamiltonian of the QCD string with quarks, corresponding to the obtained gluodynamics string effective action, where only the Nambu-Goto and rigidity terms are taken into account, is obtained. We also demonstrate that perturbative gluons propagating in the nonperturbative QCD vacuum lead to a correction to the rigidity term coupling constant.