Green functions of vortex operators
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States). Dept. of Physics
In this paper, we study the euclidean Green functions of the 't Hooft vortex operator, primarily for abelian gauge theories. The operator is written in terms of elementary fields, with emphasis on a form in which it appears as the exponential of a surface integral. We explore the requirement that the Green functions depend only on the boundary of this surface. The Dirac veto problem appears in a new guise. We present a two-dimensional “solvable model” of a Dirac string, which suggests a new solution of the veto problem. The renormalization of the Green functions of the abelian Wilson loop and abelian vortex operator is studied with the aid of the operator product expansion. In each case, an overall multiplication of the operator makes all Green functions finite; a surprising cancellation of divergences occurs with the vortex operator. We present a brief discussion of the relation between the nature of the vacuum and the cluster properties of the Green functions of the Wilson and vortex operators, for a general gauge theory. Finally, the surface-like cluster property of the vortex operator in an abelian Higgs theory is explored in more detail.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE; Fannie and John Hertz Foundation (United States)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 1134590
- Report Number(s):
- LBL-11961
- Journal Information:
- Nuclear Physics. B, Vol. 179, Issue 3; ISSN 0550-3213
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
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