/ 97 12 00 3 v 1 2 9 N ov 1 99 7 Field Correlators in the Georgi - Glashow Model and Several Aspects of its String Representation

String representations of the Wilson loop and of the non-Abelian analog of the 't Hooft loop, defined on the string world-sheet, in the 4D Georgi-Glashow model are found in the BPS limit. In the first case, only the massless photon interacts with the string, while the interaction of the massive gauge bosons yields perimeter type terms. Contrary, in the second case, massive bosons also interact with the string, which enables one to derive the coefficient functions parametrizing the bilocal correlator of the dual field strength tensors, whose asymptotic behaviours at small and large distances are found to be in a good agreement with the observable lattice data in gluodynamics. In the recent papers 1,2 , the string representation for the 't Hooft loop average defined on the string world-sheet in the Londons' limit of the Abelian Higgs Model (AHM) has been found. In particular, in Ref. 1 it has been demonstrated that the bilocal approximation to the Method of Vacuum Correlators (MVC) 3 is exact in the Londons' limit, i.e. all the terms of the cumulant expansion higher than the quadratic one vanish. The value of the bilocal correlator has been derived from the propagator of the massive Kalb-Ramond field, and is a good agreement with the present lattice data concerning this correlator in gluodynamics 4. In this Letter, we shall proceed to the non-Abelian case of the 4D Georgi-Glashow model and study string representations for the Wilson loop average and the non-Abelian analog of the 't Hooft loop average defined on the string world-sheet. To this end, we shall make use of the same duality transformation, which has been originally proposed in Ref. 5 and then used in Refs. 1 and 2, and earlier in 6. In this way, we shall finally also find the bilocal correlator of the dual non-Abelian field strength tensors. All the calculations will be performed in the Bogomol'nyi-Prasad-Sommerfield (BPS) limit 7 of the Georgi-Glashow model, which corresponds to the Londons' limit of AHM.