Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion

Abstract

We analyze the $1/θ$ and 1/N expansions of the Wilson loop averages $ _{U_θ(N)}$ in the two-dimensional noncommutative $U_θ(N)$ gauge theory with the parameter of noncommutativity $θ$. For a generic rectangular contour $C$, a concise integral representation is derived (non-perturbatively both in the coupling constant $g^{2}$ and in $θ$) for the next-to-leading term of the $1/θ$ expansion. In turn, in the limit when $θ$ is much larger than the area $A(C)$ of the surface bounded by $C$, the large $θ$ asymptote of this representation is argued to yield the next-to-leading term of the $1/θ$ series. For both of the expansions, the next-to-leading contribution exhibits only a power-like decay for areas $A(C)>>σ^{-1}$ (but $A(C)<<θ$) much larger than the inverse of the string tension $σ$ defining the range of the exponential decay of the leading term. Consequently, for large $θ$, it hinders a direct stringy interpretation of the subleading terms of the 1/N expansion in the spirit of Gross-Taylor proposal for the $θ=0$ commutative D=2 gauge theory.