The k=2 string tension in four dimensional SU(N) gauge theories

TL;DR

This paper computes the ratio of k=2 to k=1 string tensions in SU(4) and SU(5) gauge theories, providing insights into confinement dynamics and supporting a sine law conjecture for string tension ratios.

Contribution

It presents the first lattice calculations of k=2 string tensions in SU(4) and SU(5) in 3+1 dimensions, testing a sine law conjecture and exploring implications for gauge theory confinement.

Findings

K(2)/K(1) = 1.40(8) in SU(4)

K(2)/K(1) = 1.56(10) in SU(5)

Results support the sine law conjecture for string tensions.

Abstract

We calculate the k=2 string tensions in SU(4) and SU(5) gauge theories in 3+1 dimensions, and compare them to the k=1 fundamental string tensions. We find, from the continuum extrapolation of our lattice calculations, that K(k=2)/K(k=1) = 1.40(8) in the SU(4) gauge theory, and that K(k=2)/K(k=1) = 1.56(10) in SU(5). We remark upon the way this might constrain the dynamics of confinement and the intriguing implications it might have for the mass spectrum of SU(N) gauge theories. We also note that these results agree closely with the MQCD-inspired conjecture that the SU(N) string tensions satisfy K(k)/K(1) = sin(k.pi/N)/sin(pi/N).