A Confining String Theory Derivable from Yang-Mills Theory due to a Novel Vacuum Condensate

Abstract

We discuss within the weak-field approximation and the derivative expansion how the area law of the Wilson loop follows directly from the vacuum condensate of mass dimension 2, i.e., simultaneous Bose-Einstein condensation of gluon pair and ghost-antighost pair. Such a novel vacuum condensate was recently claimed to exist as the non-vanishing vacuum expectation value of a BRST-invariant composite operator of mass dimension 2. First of all, we use a version of the non-Abelian Stokes theorem to rewrite the Wilson loop line integral to a surface integral. Then we convert the Yang-Mills theory with an insertion of the Wilson loop operator into a bosonic string theory with a rigidity term by way of an equivalent antisymmetric tensor gauge theory which couples to the surface spanned by the Wilson loop. This result suggests an intimate relationship between quark confinement and mass gap in Yang-Mills theory. In fact, the dual Ginzburg-Landau theory describing the dual superconductivity is also derivable by making use of duality transformations without using the naive Abelian projection and without breaking the global color invariance of the original Yang-Mills theory. This feature is desirable from the viewpoint of color confinement preserving color symmetry.