calculations show that the tension in an isolated static rope is proportional to the quadratic Casimir operator $C_2$ [@Bali:2000un]. The Casimir operator is only defined up to a normalization constant, but for our purpose we only need the value of $C_2$ normalized to a triplet (antitriplet) $\{1,0\}$ ($\{0,1\}$), corresponding to the tension in a single string. This is given by $$C_2(\{p,q\})/C_2(\{1,0\})=\frac{1}{4}\left(p^2+pq+q^2 +3p+3q\right),
\label{eq:scaledcasimir}$$ which thus can be regarded as the relative strength of the “rope tension”.

It is, however, possible that the energy is increased if the transverse area is constrained by neighbouring ropes and strings. This effect is very hard to estimate, and contributes to the uncertainties in the predictions from string interactions. To illustrate this problem we first look at the analogous situation in a normal superconductor. Here a longitudinal magnetic flux is confined by currents in the surrounding condensate. In an extreme type I superconductor the surface energy is small, and a tube with two flux quanta will have doubled cross section and doubled energy. If, however, the flux tube would be constrained within the same transverse area, the magnetic field energy will be multiplied by 4, but the energy to annihilate the condensate within the tube 