k-string tensions and the 1/N expansion

TY - JOUR

T1 - k-string tensions and the 1/N expansion

AU - Greensite, Jeffrey Paul

AU - Lucini, B.

AU - Patella, A.

PY - 2011/6/17

Y1 - 2011/6/17

N2 - We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.

AB - We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.

U2 - 10.1103/PhysRevD.83.125019

DO - 10.1103/PhysRevD.83.125019

M3 - Journal article

SN - 2470-0010

VL - 83

SP - 125019

JO - Physical Review D

JF - Physical Review D

IS - 12

ER -