k-string tensions in the 4-d SU(N)-inspired dual Abelian-Higgs-type theory

Abstract

The k-string tensions are explored in the 4-d [U(1)] N −1 -invariant dual abelianHiggs-type theory. In the London limit of this theory, the Casimir scaling is found in the approximation when small-sized closed dual strings are disregarded. When these strings are treated in the dilute-plasma approximation, explicit corrections to the Casimir scaling are found. The leading correction due to the deviation from the London limit is also derived. Its N -ality dependence turns out to be the same as that of the first non-trivial correction produced by closed strings. It also turns out that this N -ality dependence coincides with that of the leading correction to the k-string tension, which emerges by way of the nondiluteness of the monopole plasma in the 3-d SU(N ) Georgi-Glashow model. Finally, we prove that, in the latter model, Casimir scaling holds even at monopole densities close to the mean one, provided the string world sheet is flat.

k-string tensions and the1/Nexpansion

“…Casimir scaling of k-string tensions is found in certain supersymmetric models [24,25], 4 and, as the leading term in an appropriate expansion, in gauge-adjoint Higgs models in 2 þ 1 dimensions [27,28]. A number of scenarios other than Casimir scaling and the sine law (such as string counting, in which k ¼ k, or the bag model inspired ratio of square-root Casimirs) are already excluded by lattice simulations [2][3][4][5][6][7].…”

Monopole-Based Scenarios of Confinement and Deconfinement in 3D and 4D

“…Furthermore, since closed dual strings represent excitations of the vacuum, the mean sizes of their world sheets Σ i 's are much smaller than the mean size of the confining-string world sheet S. For this reason, closed strings and their interactions with the confining string can to the leading approximation be disregarded altogether. Within this approximation, one readily obtains Casimir scaling for the k-string tensions [95]. Corrections to this scaling, produced by closed dual strings, as well as by the deviation from the London limit, can also be obtained analytically (cf.…”

“…Hence, the minimum of S min , and therefore of S, is achieved in the case where all k weight vectors in Equation (46) are mutually different [94,95]. For this value of n, the exponential reads e…”

“…Refs. [95,116]) that the London limit allows for a construction of an exact string representation of the 't Hooft-loop average (76). Furthermore, the consistency of the corresponding [U(1)] N −1 -invariant dual Abelian Higgs model with the Yang-Mills theory in the large-N limit requires the coupling to behave with the number of colors as = λ /N .…”

“…Following Refs. [95,116], we consider here the scaling behavior λ = O(N 2 ), in which case κ stays N -independent in the large-N limit, i.e., the increase of N does not make the London limit deeper.…”