SU(N) fundamental and adjoint confining strings

TL;DR

This paper constructs string representations of Wilson loops in SU(N) compact QED in 3D and 4D, analyzing confining strings, string tension, and effects of the theta-term, with results applicable in strong-coupling regimes.

Contribution

It provides exact and large-N limit constructions of confining strings in SU(N) compact QED, including calculations of string tension and higher-order terms in the string effective action.

Findings

String representations are constructed explicitly for fundamental Wilson loops.

The string tension is fixed in the weak-field limit, providing a new way to determine it.

Critical theta-values for crumpling are identified in 4D, relevant in strong-coupling confinement regimes.

Abstract

String representations of the Wilson loop are constructed in the SU(N)-version of compact QED in three and four dimensions. This is done exactly in the case of the fundamental Wilson loop and in the large-N limit in the case of the adjoint Wilson loop. Using for concreteness the three-dimensional fundamental case, it is demonstrated how the resulting SU(N)-generalization of the so-called theory of confining strings can be obtained in various ways. In its weak-field limit (corresponding to the limit of low monopole densities), this theory enables one to fix the value of the string tension, which cannot be fixed when deduced from the mean magnetic field inside a flat contour (the derivation of this field is also presented). Moreover, the obtained theory enables one to find also the coupling constants of terms in the expansion of the nonlocal string effective action, which are higher in the derivatives than the Nambu-Goto term (some of these terms vanish at the flat surface). In the four-dimensional case with the theta-term, the critical values of the theta-parameter, at which the problem of crumpling of large world sheets might be solved, are found in both the fundamental case and in the large-N limit of the adjoint case. These values are only accessible provided the electric coupling constant is larger than a certain value, in accordance with the known fact that confinement in the four-dimensional compact QED holds in the strong-coupling regime.